# Talk:Entropy/Archive 2

(Redirected from Talk:Entropy/Archive2)

## Thermodynamic definition

In reference to this: "${\displaystyle \delta Q}$ of energy transferred by heating is denoted by ${\displaystyle \delta Q}$ rather than ${\displaystyle dQ}$, because Q is not a state function while the entropy is."

That seems really unclear to me. What is the significance of Q not being a state function. Also, it seems like Q *is* a state function, after all, it doesn't matter how the heat got to the system, as long as it is there, right? the δ notation still confuses me, as I've taken plenty of math and have never seen a δ be used in algebra or calculus. Fresheneesz 10:55, 4 April 2006 (UTC)

Heat isn't a state function since it's not a function of the thermodynamic state. I can figure out the change in energy between thermodynamic state A and state B, because energy is a state function, but I cannot know how the energy changed (What proportion was heat and what proportion was work?) unless I know the transformation taken between the two states. Heat and work are path functions. However, I agree that the whole inexact differential stuff is confusing, even for the initiated. Surely, its easier to understand ${\displaystyle \Delta E=Q+W}$ than ${\displaystyle dE=\delta Q+\delta W}$ Nonsuch 19:18, 4 April 2006 (UTC)

Heat cannot be a state function because it is defined in the first law of thermodynamics as a transfer, rather than a stored quantity. Internal energy is stored. The term heat is used to describe energy transfers induced by temperature differences.

The way I think of it is that an exact differential is an infinitesimal change, while and inexact differential is an infinitesimal amount (remember that a differential is just the limit of a difference). Commander Nemet 04:56, 7 June 2006 (UTC)

In the Units section, perhaps one should also include the statistical definition of entropy, σ=lng, and maybe even the extended one. --rhevin 19:36, 23 May 2006 (UTC)

That is only the Boltzmann definition. What is the extended one? LeBofSportif 07:23, 24 May 2006 (UTC)
What I mean was the definition of entropy when the system is in thermal contact with a reservoir, ${\displaystyle \sigma =-\sum _{s}^{}{P_{s}\ln P_{s}}}$, that is, not an isolated system. --rhevin 08:13, 24 May 2006 (UTC)

## Disorder, Multiplicity, and Thermodynamics

If someone, not a scientist, asks "What does Entropy measure?" then as long as the person doesn't need to do calculations then there is nothing wrong with talking about entropy as a kind of disorder. It fits naturally - Why does a salt crystal dissolve in water, ever though that is an endothermic process?
Well, the dissolved state has much higher entropy because the ions can spread out in the whole liquid.
It is very hard to explain entropy well while being totally accurate about it, unless the reader is prepared to do some physics questions to deepen their knowledge. So if you can make the article more comprehensible, and more accurate at the same time then go for it. But its not easy. Btw, The S.I. unit of disorder is a malarkey (M). :-P LeBofSportif 10:24, 7 June 2006 (UTC)
Astro, you wrote that
Entropy is a key physical variable that describes how heat moves between physical systems, "disorder" is not - in all my years of thermodynamics, from my classes in grad school to my career as a physicist, I have never measured or calculated "disorder."
You might like to consider, firstly, the entropy of mixing, where an important entropy change happens with no heat transfer (cf the salt dissolving example); or, secondly, entropic force, where the elasticity properties of polymers are modelled in terms of their configuration entropy as a function of length.
Both cases illustrate, it seems to me, that thinking about entropy in terms of multiplicity of states, and directly thence in terms of disorder or mixedupness can be a very useful way to go.
The article also used to explain that the entropy of statistical thermodynamics can be identified with
the amount of uncertainty that would remain about the exact microscopic state of the system, given a description of its macroscopic properties.
That would seem to me precisely accurate, and another very helpful statement to encapsulate how entropy in statistical thermodynamics can be understood. I'm not clear why it was cut. -- Jheald 16:11, 7 June 2006 (UTC).

## Article is now 46 kilobytes long (the limit is 32)

I just finished added parts to the history section. The whole page seems to be too unwieldy. I propose breaking up the article as follows:

In this manner, the main entropy page will have mini-articles (with {{see:main}} links attached). See: the thermodynamics and gravitation articles for example; these are one’s I’ve helped to break-up in the past. If anyone wants to do this, by all means do so; this is just a suggested outline. I’ll let this idea marinade for awhile.--Sadi Carnot 04:20, 5 April 2006 (UTC)

I think it would be nice to have a page with a overview of all entropy 'stuff' (short version of current one), with links to specific pages where things are discussed in detail.Lakinekaki
Hey! It seems I cant read! You proposed the same thing. Cool. :O) Lakinekaki
I would broadly agree, but would point out that there already exists a page on the arrow of time - why not use that page instead of creating a new one? Mike Peel 14:16, 10 April 2006 (UTC)
Thanks for the tips; I'll take these into account (working on break-up slowly). --Sadi Carnot 00:26, 11 April 2006 (UTC)

Done with clean-up/break-up of article. Almost nothing was deleted; only moved around. The main article is now only 5 printable pages (instead of about 15) and gives a nice overview. I hope everyone likes the result.--Sadi Carnot 03:40, 11 April 2006 (UTC)

## Which Carnot

The History section is a little unclear. Both Sadi and Lazare are mentioned but the timing doesn't quite mesh.

• 1803 - Lazare publishes paper
• Three decades of Carnot's theorem
• 1823 (???) - Lazare dies
• 1824 - Sadi graduates and writes paper, including developing the Carnot heat engine principles (although this is not wikilinked)

I don't know much about the subject, but to me it just doesn't quite mesh.

There doesn't seem to be any WP reference to Carnot's theorem (not this one). Perhaps all that needs to happen is this part/sentance is removed. I'll leave it to someone with more scientific history knowledge to decide. Frelke 06:19, 7 April 2006 (UTC)

The reference is the following:
References
1. ^ Mendoza, E. (1988). Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. New York: Dover Publications, Inc. ISBN 0486446417.
I'll try to clarify it more shortly; basically, Lazare Carnot (Sadi's father) wrote some conservation papers with "entropy" concept precursors imbedded; the year after he died his son (Sadi Carnot) wrote "Reflections on the Motive Power of Fire", the paper which started thermodynamics as a science, and in which the 2nd Law was first formally stated, and upon which Clausius built his differential form of entropy. In other words, both the father and the son had their own theorems, the father’s theorem was well-known in 1830, but the son’s theorem remained unknown until the 1840’s and 50’s. --Sadi Carnot 15:17, 7 April 2006 (UTC)

## Reverting "Entropy"?

Does reverting "Entropy" increase its entropy? Oneismany 05:29, 4 May 2006 (UTC)

## Entropy, order, and disorder

I removed the following paragraph as being misleading at best:

It should be stressed that entropy and disorder are different quantities (simply because disorder is undefined subjective quantity while entropy has strict mathematical definition). Classic example of increase of entropy with decrease of "disorder" is gravitational collapse of uniform "disordered" hydrogen gas left from Big Bang into "more ordered" star systems and planetary systems. Another classic example is evolution - creation of "order" (by random mutations) in small portion of open system at the expense of increase of entropy elswhere.

Stars are not more ordered than the gas from which they condensed because stars get very hot as they collapse. The sentence on evolution isn't wrong, but it doesn't demonstrate that disorder and entropy are different. Nonsuch 16:09, 9 May 2006 (UTC)

Oops, guess what - you are wrong again :-). You forgot to define "order". Did you pay attention to what I actually said - I said that "order" is undefined quantity. That is why I put it in quotation marks. So, again lack of definition resulted in sloppy statewment on your part and as a result - instead of clarifying you made it look even less clear. So, please DEFINE your terms (specifically the term "order") before you try to make a statement remotely relating to "order".
Sincerely, Enormousdude 01:56, 11 May 2006 (UTC)
Good work. A suggestion would be to replace the former with: in ideal gas systems entropy can be modeled in terms of the order of the system, i.e. the probability of states to which the dynamic system may evolve. Subsequently, as the inverse of order is disorder, entropy, under certain circumstances, can be defined in terms of disorder.--Sadi Carnot 17:23, 9 May 2006 (UTC)
So far, I don't see any good work here (only inability to clearly define the subject of discussion on the party you refere to as of "doing good job" and a quick political flexibility on your side of bending toward that said party (which is never welcomed in science, by the way) - that is all I see here).
Reading non-political part of your message, I welcome your desire to define "order". It (a definition of the term "order") is vitally important here (and I have some definite thoughts about it, but would like to listen to others first), but because "order" is subjective term, it (a definition of "order") can be quite subjective - and thus not easy task to do, though. All misconceptions about entropy stem from this definition (actually from the lack of it). Let's talk about such definition.
Enormousdude 01:56, 11 May 2006 (UTC)

I'm cutting this paragraph, not least because IMO to get into the detail of this discussion is inappropriate for the introduction above the contents list. IMO the introduction is clearer, and gives a more balanced first introduction to the concept of entropy without this paragraph; and IMO even without the paragraph, it is already right at the limit for being as long as it desirably should be.

Also, IMO we already indicate how the intuitive notion of "disorder" or "mixedupness" is to be more precisely understood, namely as

the amount of uncertainty that would remain about the exact microscopic state of the system, given a description of its macroscopic properties.

That is a definition of how mixed up we consider the system to be. -- Jheald 09:13, 11 May 2006 (UTC).

## Second Law mathematically provable?

Also I reverted the last sentence of this paragraph:

An important law of physics, the second law of thermodynamics, states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. This law mathematically follows from the accurate mathematical definition of entropy.

Unfortunately not true. Additional assumptions are necessary. Nonsuch 16:09, 9 May 2006 (UTC)

Oops, again miss of your shot :-). As I explained earlier, "indistinguishability" of indistinguishable states (=old states system occupied before, and equivalent new states which became available) is the only additional assumption needed (provided that the total energy is conserved = which is guaranteed in the very beginning by the words "entropy of isolated system..."). Shall I stress somewhere that "identical" states (new states) are required to be identical (to the very same old states the system occupied before entropy change)?
Also, on unrelated to your input side, such words in the previous edition (which you are so eager to bet your vital organs under axe on that you revert back to it without editing or even thinking) as "tend to ..." - are also ill defined, and therefore must either be completely avoided or clearly defined (shortly before or shortly after their usage) - which is not done by you either.
As I said, be accurate in your words - simply because ill definitions (or worse - lack of any definition) result in ill undertanding (and in complete lack of thereof when definitions are absent).
Or shall I assume that you just blindly revert correct statements without thinking (or even reading) them - just because you just like edit war? That might be the case here (and by the way, I see it happens with you again and again - look over other your late reverts which are also incorrect).
Well, then again it just speaks for itself (both for your lack of exprtise and thus for low reputation of wikipedia, because you (and other non-educated editors) cut additions of others without thinking or correcting. As I said, earlier when you (and your team) reverted many times my correct definition of force F=dp/dt (see force article) these blind reverts simply resulted in spread of ignorance and in more confusion. (But, may be the Wikipedia was meant to spread ignorance? Otherwise - how to explain low quality of information dominating it??!)
Sincerely, Enormousdude 01:56, 11 May 2006 (UTC)

Dude, I look forward to reading your proof of the 2nd law starting from the classical dynamics of an isolated system and indistinguishavility in a main stream physics journal. In the mean time you're talking utter nonsense. There is no such proof, at least none that is widely accepted. One runs into all sorts of deep philosophical and physical difficulties. At some point you have to assume molecular chaos, or corse graining, or stochastic dynamics or some procedure that throws away information. And remember that your purported proof has to be resilient against attacks by Maxwell daemons and other intelligent opponents. This is a not a trivial problem. Nonsuch 03:17, 11 May 2006 (UTC)

Guess, what? This is EXACTLY because disorder is undefined quantity. There is no need to philosophise here - simply because there is no objct of philosophy yet (order or disorder). As I said MANY TIMES - definitions are VITAL to understand what you are talking about. Without definition of order/disorder there is not much you can say about its relationship to entropy. So, instead of spending time on sensless blah blah blah (live that for philosophers, please) define order (or disorder). Enormousdude 16:16, 11 May 2006 (UTC)
Enormous is one of the worst scientific contributors I've seen in a long time; even most of the anons are better contributors.--Sadi Carnot 04:10, 11 May 2006 (UTC)

Not true. My many definitions are now at the hearts of many articles of Wikipedia - which before me were incoherent mumbo-jumbo without clear definitions. I am proud that my expertise can improve the quality of Wikipedia which is quite poor (especially compared to real encyclopedias - like old but good soviet encyclopedia, or Britanica or to encyclopedia of physics I have).

By the way, many of my (later removed by Nosuch and others) definitions are exactly the same as in these encyclopedias - I recently checked . These encyclopedias were written not by amateurs as Wikipedia is written by, but by the experts in their fields - that is why they (printed encyclopedias) are so good and concise. Especially when I compare my definitions with good textbooks or US encyclopedia of physics. I intentionally do not quote these credible sources till enough ill-justified reverts accumulate and long discussions go nowhere exactly due to removal of my clear definitions and replacement them back by nonsense mumbo-jumbo).

If I have spelling and sometimes grammatic errors - yes, of course I do - because English is not my native language. Despite that, I have published (and continue to publish) plenty of scientific papers in English. Scientific journals accept them just fine. What surprises me that even you and many others who claim English to be their native also do a lot of spelling and grammar mistakes(!). Do you want to quote yours? Just let me know (in general, I do not like to get involved into personal fight and consider edit wars just a waste of time, but if you provoke me I may be forced to). So, feel free to correct my grammar and spelling instead of reverting back to undefined nonsense. That is the exact spirit of Wikipedia - to jointly increase knowledge rather than blindly delete it. Sincerely, Enormousdude 16:16, 11 May 2006 (UTC)

To underline what Nonsuch wrote, any "proof" of the Second Law has to deal with the question of Loschmidt's paradox. The nearest thing we have to such a proof is the H-theorem. But this relies on a number of often unstated assumptions:
1. that useful information is destroyed, e.g. by collisions (which can be questioned).
2. it relies on a non-equilibrium state being singled out as the initial state (and not the final state), to break the time symmetry
3. strictly it applies only in a statistical sense, namely that an average H-function would be non-decreasing.
Points 1 & 2 are non-trivial statements about the physics of the system (or perhaps more accurately, the modelling of the system). Claiming that "This law mathematically follows from the accurate mathematical definition of entropy" buries what is really going on, to an extent which is positively misleading. -- Jheald 08:48, 11 May 2006 (UTC).

Guys, please first clearly DEFINE your terms to avoid endless (and sometimes incoherent) mumbling. Start with the definition of order/disorder (you are velcome to read my correct but deleted again statement about relationship between entropy and disorder). Sincerely, Enormousdude 16:16, 11 May 2006 (UTC)

You lost me. Which term do you wish to define? Disorder? Disorder is a common English word, and as such does not have a precise definition itself, except to the extent that we think of entropy as a measure of disorder. We talk about disorder because it's an intuitive concept, but we use entropy because it's mathematical defined. What, exactly, do you think the article is missing? (And it's Nonsuch, not "nosuch") Nonsuch 17:24, 11 May 2006 (UTC)

Finally, a sort of consensus on the horizon. That is exactly what I meant by adding the edit which says that entropy and disorder are different things. Indeed, you see - there is no accurate definition of disorder. Obviousely, without such definition one can not say that increase of entropy results in increase of disorder (or vice versa). My example about collapsing gas shows that if to use ill-defined "intuitive order" then it may appear that such "order" is sometimes decreasing but sometimes increasing with the increase of entropy. And all kind of misconceptions about second law, arrow of time, etc in relation to disorder arise - simply as a consequence of lack of accurate definition of disorder. Indeed, suppose a gas which was filling space (say, a container of a few light years across) gravitationally collapses into very small volume (say, into a star of a few light seconds across). Which system is more "ordered" then - the first one where gas was evenly distributed over entire container, or the second one in which practically all gas occupies only 1x10^-22 part of the same container? What does your "intuitive disorder definition" tells?

Sincerely, Enormousdude 22:06, 11 May 2006 (UTC)

The problem is that, although the issues have been discussed ad infinitum, the article continues to have a confusing and ambiguous view on "disorder" and "randomness". Entropy canNOT be conceptualized as any sort of disorder. And as long as this article continues to introduce and explain entropy in terms of "disorder" and "randomness", this talk page will continue to get all-new users who profess its stupidity/confusingness.
I've put up an explanation on the terms "disorder" and "order" in the definition. It will no doubt be removed, as similar arguement are explained in passing in a couple different sections. I think we should work to keep this page free of explanation involving "disorder" and "randomness" AND note that those terms are misleading (and in fact wrong).. but still seen everywhere. Fresheneesz 09:09, 1 June 2006 (UTC)

## The Ice Example Picture

Ice melting - a classic example of entropy increasing. Is it really? Can't one contrive reversible melting simply by putting ice in water at 0 deg C? Surely gas expanding into a vacuum is a much better example? LeBofSportif 19:48, 12 May 2006 (UTC)

If the ice is melting (As presumable it is, because the surroundings in the picture are at room temperature) then entropy is increasing. But, yes, perhaps a better example could be found. Nonsuch 18:45, 24 May 2006 (UTC)
It's very difficult to show gas expanding into a vacuum in a way that most people will relate to. However, many people have experience with pop cans. May I propose [1] as a candidate?Alex Dodge 19:57, 17 June 2006 (UTC)
Almost every chemistry textbook use ice (crystalline form), water (liquid form), and vapor (gas state) H2O molecule pictures and diagrams to show and contrast systems with high entropy and low entropy. The second common pictorial example is to show dots (of gas molecules) expanding in a system subjected to a volume increase. The ice picture example is the most informative.--Sadi Carnot 23:16, 19 June 2006 (UTC)

## Randomness and disorder

"randomness and disorder" has once again been added to the definition. I must stress that we cannot leave "disorder" and "randomness" undefined in this context, simply because the informal use of such words does not in any way shape or form describe anything about entropy. Although I deeply dispise the attachment of the three words "disorder", "randomness" and "entropy", I will simply add a formal definition for randomess and disorder into the intro. Fresheneesz 07:16, 31 May 2006 (UTC)

## entropy and the Time Machine

This page says that the the book The Time machine is based on entropy, but theres no mention of that on the page for that book. Fresheneesz 09:02, 1 June 2006 (UTC)

According to this site http://www.entropysimple.com/content.htm Entropy is not related to information entropy and is not disorder. Since the first paragraph of the article directly contradicts this site I stopped reading in utter disgust. I almost threw up. I was worse than goatse man. —Preceding unsigned comment added by 64.40.60.1 (talkcontribs) 18:29, 16 June 2006

I agree, the introduction is all cluttered up; Clausius would probably throw up too if he saw it. I will try to clean it.--Sadi Carnot 23:18, 19 June 2006 (UTC)
@64: People obviously seem to like the article you cite enough that some of the points it makes keep on getting brought up. But IMO some of the contentions it makes are seriously misleading, and actually get in the way of a deeper, more complete, more systematic understanding of the concept of entropy. For example:
• Entropy change exclusively relates the the dispersion of energy. This is false. See for example the discussion in the paragraph "Disorder, Multiplicity, and Thermodynamics" further up this page. Restricting entropy changes to dispersion of energy is too narrow, too restrictive. In very many cases the dispersion of energy is far and away the most important contribution to entropy change -- but not in all cases. That is why entropy increase is better thought of in a more general way, as a dispersion of certainty about the state of the system.
• "From the 1860s until now, in physics and chemistry (the two sciences originating and most extensively using the concept) entropy has applied only to situations involving energy flow that can be measured as "heat" change, as is indicated by the two-word description, thermodynamic ("heat action or flow") entropy." This is false, a particularly concrete and definite version of the false assertion above.
• Entropy in statistical thermodynamics is quite different from information entropy. This is false. The correct relation between the two is that information entropy is the more general, more fundamental concept. It can be used as a measure of uncertainty of any kind quantified by a probability distribution. Statistical thermodynamic entropy is a special case, which arises when information entropy is used to measure 'the amount of uncertainty that would remain about the exact microscopic state of the system, given a description of its macroscopic properties'.
I could go on (eg entropy and probability; entropy and disorder...); but with luck you get the picture.
However, I do agree with Sadi that the lead paragraph as it stands tonight is definitely not good. IMO it was significantly clearer as it stood several weeks ago. -- Jheald 01:23, 20 June 2006 (UTC).
Jheald, what are you doing? You just reverted all of my work? Where did the overview section go? Where did the entire intro go? Where did the four new definitions go? Please clarify?--Sadi Carnot 04:42, 20 June 2006 (UTC)
I'm sorry, when I wrote that "the lead paragraph as it stands tonight is definitely not good", I hadn't realised that was your edit I was reading. Jheald 05:11, 20 June 2006 (UTC).
The article at Entropy Is Simple that everyone refers to was written by a chemist - i.e. a scientist who holds a Ph.D. This means that generally we should lend him our ear, as what he has to say holds authority (what is the point of becoming an expert otherwise?) Aside from his own credentials, the way he presents Entropy is exactly the way it is taught in physics classes (and as physics is the discipline upon which all others rest, _it_ is the standard, not "writers who are not scientists, and joking mathematicians" as the article points out): Entropy is a tendency of energy to move from one place to another. Period. This is simple, quantifiable, and allows a straight-forward presentation of the material to any audience, whether or not they have a degree in a scientific field. All of these other holistic approaches to Entropy are impractical. They are useless when engineering real systems. Thus, I strongly disagree with Jheald's statement that the Ent.Is Simple material be brought into question by this article - Wikipedia is an online encyclopedia, not a peer-reviewed scientific journal and it is therefore well served by the inclusion of great material such as the Ent. Is Simple website. Astrobayes 20:20, 22 June 2006 (UTC)

## Negentropy, Ectropy, Syntropy, Extropy

According to the IEEE, the use of Negentropy and similar terms is now strongly deprecated.

Such words compound the conceptual difficulty people have with the meanings of entropy, with what is in effectively conceptually a double negative -- starting with entropy, ie the information you don't have, going to negentropy is then the information you don't not have.

Almost always this is not a good way to go, and such terms just get you into larger and larger knots. Schroedinger used negentropy in quite a specific way, for the order that could be built up inside a living system, possible because of the entropy increase being dumped outside the cell. But Brillouin's use was a mess, very confusing.

These coinages have never taken off, and deserve to wither. Negentropy perhaps rates a mention in "see also". The rest really just deserve the ash heap of history -- *most* definitely they do not deserve high-profile special highlighting up at the top of what is meant to be a very simple very mainstream overview article.

-- Jheald 05:09, 20 June 2006 (UTC).

These terms I don't really care about; they should, however, go in an end paragraph for the sake of orgnization. If you will note the history section, someone else put the first one in, so I just clarified a bit with the others. Also, I started a new header for the information entropy links and stuff to go.--Sadi Carnot 05:14, 20 June 2006 (UTC)
No. The terms should just die. They're just useless cruft. Bury them in the article on negentropy if you feel the overwhelming urge that they have to be linked to from somewhere. -- Jheald 05:40, 20 June 2006 (UTC).

## New intro: critique

Although the concept of entropy is primarily a thermodynamic construct, it has since expanded into many different fields of study, such as: statistical mechanics, statistical thermodynamics, thermal physics, information theory, psychodynamics, economics, business management, and evolution, to name a few.

Entropy, in so far as the term is being used coherently at all, rather than just as a synonym for 'decay' or 'disorder', refers in those contexts at most to Information entropy, not Thermodynamic entropy -- apart of course from entropy in statistical mechanics, statistical thermodynamics, thermal physics -- which is thermodynamic entropy.
Hiding that disambig way down at section 5 of the main body would be so useless as to be a joke. Jheald 05:25, 20 June 2006 (UTC)

Clausius coined the term based on the Greek entrepein meaning "energy turned to waste".

No it doesn't. There's no connotation of "energy" in en-trepein; nor is there any connotation of waste. trepein means "turning" or "changing" or "transforming", and en just signifies the content of that internal to the system.
That's the etymology. But I don't think it helps one to understand the concept much. -- Jheald 05:38, 20 June 2006 (UTC).
Jheald, we have to think along the lines of the general reader. I would guess the following percentages as to who visits this page: chemistry people (40%), thermodynamic people (20%), physicists (10%), information theory people (5%), and other miscellaneous people (25%). So, yes I agree with you, but we can't have a clutter of 4-5 disambig links and redirects at the top of the page. As to the top insert, I personally own at least 3 books on each topic that utilize the concept of entropy in some way or another; however, I will trim it a bit to see if that helps? The main thing is that we need a concise intro paragraph leaving enough room to see the table of contents. --Sadi Carnot 05:50, 20 June 2006 (UTC)
I think you radically underestimate the traffic for entropy meaning information entropy, with relevance to mathematics, statistics, electrical engineering, data compression, inference and machine learning, fractals, ecology, etc, etc.
The important think is to let people who don't want thermodynamic entropy know that this is not the article for them. To that end, I don't think 2 lines of disambig text is excessive. -- Jheald 06:06, 20 June 2006 (UTC).

You could be right, but I am quite certain that there are more chemistry students who want to know about entropy than any other type of student. Also, why don't you merge these two articles into one, i.e. [1]+[2]="New name"? --Sadi Carnot 17:06, 20 June 2006 (UTC)

Not a good idea, IMO. The second article was created because there was a genuine value in creating it, by triaging together some substantially overlapping material which was taking root in a number of different articles. It wasn't me that made it, and IMO it could use more than a little sorting out; but I think it was absolutely right that the it was created. The relationship between the two uses of the word entropy is of genuine interest; and it hangs together as a topic in its own right. Having the separate article benefits by giving the space to explore various connections from a number of different angles; it also allowed detailed material to be removed from a number of articles (including this one, and information entropy) in which, while perhaps interesting, it was duplicative and only of peripheral importance.
I have to say, you seem very much to be approaching this from the viewpoint of a physical chemist. I wonder if you realise just how strongly for, say, an electrical engineer, the idea of information entropy is of absolutely foundational significance to the whole of communication theory; whereas the idea of thermodynamic entropy may be completely irrelevant.
If somebody is looking up entropy to learn about, say, entropy encoders, then thermodynamic entropy has no bearing or relevance to their question. It is purely a distraction and a confusion. But if they are not a chemist, they might not know that, when they put their search into wikipedia. That is why, IMO, the article should have a rather more talkative disambiguation slug at the top than normal, to spell out the point quite explicitly then and there, that this is not an article about information entropy; information entropy is something rather different; but there is another article which examines connections between the two.
There is only one key meaning of gravitation in physics. But there are two key uses of the word entropy in science: thermodynamic entropy and information entropy; and it is only when somebody has got really quite a good grasp of each use separately, that it really makes any sense to try to bring the two together. That is why the bringing-the-two-together material IMO does deserve a separate article of its own. And why IMO the more extensive disambig text I put up would still be rather better to have at the top of the article. -- Jheald 20:19, 20 June 2006 (UTC).
Unfortunately, Jheald my friend, most people have a good grasp of neither and it has taken me the better part of a graduate education in physics to really understand and appreciate the usefulness and contexts of both Entropy and information theory, as two distinct branches of tools. The intriguing thing about so many concepts in physics - Entropy included - is that the natural human desire to quickly know and understand a topic is not possible for many concepts in the natural sciences without compromising some fundamental aspects of the theory or model being presented... and at that point you're no longer presenting the model as it truly is. Gravity is brought up as the poor old football in these discussions but the funny thing is that while most people think they have a handle on gravity, few do. The more we learn about it the more we find out that Newton's picture of gravity is equivalent to Bohr's picture of the atom. Revolutionary in it's time, but appropriate in 2006 for basically elementary school children. So too it is with Entropy. And in the interest of the general reader, we should delineate and properly describe the two primary meanings of Entropy used here. Far too many people make assumptions on physical systems based upon information theory. We can serve the readers of Wiki by improving the quality of this article thus. Astrobayes 21:54, 23 June 2006 (UTC)

## GA awarded

It is a pleasure to read since it is pure physics taken to an easy reader's understanding. I was bad in physics and would have hoped my teachers would read that so they would actually teach this matter well. Thanks ;) Lincher 01:10, 22 June 2006 (UTC)

I agree that most of the article is well-written, and easy to understand the way the material is presented, however it is not purely physics and that is important to note. Things like informational Entropy and disorder are neither useful, nor used, ideas in physics. What in this article is described as "disorder" is (meant to be equivalent to) what is known in physics as multiplicity or "degeneracy of states," rather and they are not the same thing. Informational Entropy is something that is useless to most physicists, unless you are speaking of a field like quantum computing. The challenge to improving this article though is that there are many more non-scientists with strong opinions about fields in which they are not authorities, whom are quite often unwilling to allow the expertise of an authority to contribute to an article such as this, than there are actual authorities on the subject. In short, some of the best edits get reverted. For now, consider this article an average, basic review. It's quality will improve with time - I plan on contributing to that effort as well. Astrobayes 20:35, 22 June 2006 (UTC)

## Discussion on Article Improvements and Quality

Astrobayes, with your user id I can't help finding it a bit ironic that you seem so militantly opposed to E.T. Jaynes's Bayesian take on statistical thermodynamics!
"Things like informational Entropy ... are neither useful, nor used, ideas in physics". This is false. Can I refer you to the page on Maximum entropy thermodynamics? Also especially note the magazine article by Lorenz in the links at the end, and the papers by Dewar. Many physicists find the Bayesian/MaxEnt point of view very useful in sharpening and simplifying how they think about entropy in physics; particularly for the creating of a statistical mechanics of non-equilibrium systems.
"What in this article is described as "disorder" is (meant to be equivalent to) what is known in physics as multiplicity or "degeneracy of states," rather and they are not the same thing." If more of a system's microscopic states are compatible with a particular macroscopic description, it seems entirely appropriate to describe those states as therefore being more "mixed up". (Or, equivalently, if there is more uncertainty remaining, given the macroscopic description). Isn't it? What is the logical step you think is being missed in such an assertion? Jheald 14:42, 23 June 2006 (UTC).
While I do agree with you that the words "disorder" and "mixed up" make the description of a degenerate state more palatable, they are not physically correct descriptors. They are wholly anthropocentric, for to say something is "disordered" means that you have chosen some standard for order, and that is a completely human concept. When I'm doing a calculation to determine the characteristics of a physical system it is useless for me to say it is disordered or not (for example, if I asked you how disordered a system is what would you say? Would you say the "order factor" is 10? Or 20? But 10 or 20 what? What is the unit of "disorder" and what fundamental units is it composed of? The problem is... there is no such thing as an "order" quantity in physics. It is a conceptualization tool for statisticians, writers, and computer scientists - not a real variable... but Entropy, a heat transfer at a specific temperature - that can be quantified, measured, and described). And these real concepts help me becuase to know the level of degeneracy means that I can properly calculate things like scattering cross-sections, etc. It is challenging to write a palatable yet educational article on this topic - I can appreciate that. So it is especially important that we reinforce the fundamental definitions of these important concepts. Keep up the great questions! This is a valuable discussion and I hope to greatly improve the quality of this article from them. Astrobayes 16:06, 23 June 2006 (UTC)
"There is no such thing as an "order" quantity in physics". I disagree. When a description of a macroscopic state is compatible with only a very small number of microstates, I think it is entirely reasonable to call the macroscopic state "ordered" based on that fact alone. But when there are very many microscopic states compatible with the macroscopic state, it seems reasonable to say just because of that fact that the system is "mixed up" - there is much more uncertainty about the true microscopic state of the system, given the macroscopic description.
You asked how one can objectively quantify such uncertainty in a well defined manner. The classic measure in information theory is to calculate the Shannon entropy. So we do that, and we have a number which exactly matches the entropy of statistical thermodynamics.
That's why I think it does (or can) make sense to relate "mixedupness" directly with entropy. But you're clearly not happy with this. Can you put your finger on why - is there something you think isn't fully captured in the notion of "mixedupness" just by the idea of uncertainty, and can you quantify it? -- Jheald 17:01, 23 June 2006 (UTC).
I am speaking of the behavior of matter and energy in the material world whereas information theory has little to do with characterizing the physical properties of the material world. I.T. deals with the interpretation of how we gather information about the material world, which is an entirely anthropocentric framework. Entropy in the reality of the physical world and information theory are not equivalent. It's simple: Entropy is a heat transfer at a specified temperature. You can measure it. It has units of Newton-meters per Kelvin (which is the amount of work done per unit temperature). But in what way is this "disorder" you speak of quantified in terms of fundamental physics? If you read the peer-reviewed literature on information theory (and I have) Entropy is handled about as carefully as an ape handles china. You'll find that to fit everything into the i.t. framework, the i.t.ers have to invent things like the Fisher function, and then __define__ entropy as the integral of it. In physics (i.e. the reality of the material world), we don't define and redefine Entropy. It's a heat and we measure it. But yet, confusion in some people still exists.
This is explicated in the statement above that you _relate_ Entropy to disorder. That's just it... the _relation_ gives you a decent elementary understanding, but there is not an _equivalence_ between the two. That requires a greater understanding. This is a problem equivalent to the Bohr picture of the atom. Sure, it's fine to tell elementary school children that electrons orbit atoms in shells, but in reality they do nothing of the sort. In reality, they don't orbit but rather exist in a infinite number of locations within clouds of vastly different shapes given by their quantum distributions as determined by the energy of the atomic state. This is the "grown up" understanding of atomic orbits. So when are we going to start writing and promoting the "grown up" understanding of Entropy? It's rather insulting to people's intelligence to present Entropy in any way other than heat change divided by temperature. I do wish to improve this article's quality but since I believe my edits would all get reverted, I'm going to spend a great deal of time researching quality improvements and making sure I have peer-reviewed citations for them. Here is one that illustrates the problem of why Entropy and disorder are *not* equivalent <-- in this case, if you view Entropy as "disorder" you completely fail to characterize the system, a perfect example of why the information theory view of Entropy is not useful for characterizing the material world. Any suggestions you have that would help improve this article, I gladly welcome. And thanks for the great discussion! :) Astrobayes 18:35, 23 June 2006 (UTC)
Astrobayes, I'm afraid you're wrong, or at least very old fashioned. To pick out one fallacy, the unit issue is a non-starter. The measurement of thermodynamic entropy in Newton-meters per Kelvin is an historical accident. It is perfectly reasonable, and very common in theoretical work, to measure thermodynamic entropy in nats. The conversion factor between conventional and natural units of entropy is called Boltzmann's constant. Nonsuch 19:26, 23 June 2006 (UTC)
You're right about me being "old fashioned," in a sense. I am sticking, strongly, to the fundamental physics. However, nothing I've said is incorrect thus far: Entropy and disorder are not equivalent (many, many processes can have a large entropy increase while become more ordered - and the reverse is true as well where "disorder" outpaces Entropy - I provided a peer-reviewed journal article link above to illustrate an example of this), Information Theory is about interpretation - which is anthropocentric. I do understand and appreciate this because I am a big proponent of using Bayesian analysis, which is a normalization of frequency statistics based upon a particular model being considered to interpret the results. It is ironic that the Bayesian approach can serve to filter the very discipline which developed using its concepts: information theory. As a physicist, the difference between all of these disciplines is clear to me but I certainly understand and appreciate how from a third person view, all of these issues look to be equivalent. Because of this reality I know have chosen a very uphill challenge by even suggesting an improvement to the quality of this article. That's ok, I like a challenge and I enjoy working with others to improve something. This discussion is running long, but I hope what I'm saying here is getting through: Entropy and disorder can be thought to be analagous but they are not, in fact, equal. The peer-reviewed literature in chemistry and physics supporting this assertion is overwhelming. Astrobayes 21:13, 23 June 2006 (UTC)
Astro, I haven't (yet) been able to get access to the full text of the article you cited, but from reading the abstract my impression is that its thesis is very similar to making the following argument, to say:
"Okay, so at room temperature, if I leave an ice cube in water, the ice cube melts, entropy increases (as it must), and disorder increases. But suppose the system were actually at a supercooled temperature, below 0°C, what would have happened then? Entropy must still be increasing; but this time it's the water that freezes, the ice cube gets bigger, the system is becoming more ordered... So increasing entropy can sometimes be related to decreasing disorder"
Well, my answer is that it still makes sense to identify entropy and disorder; but the example shows that you may have to be more careful than you might have first imagined, when you are thinking about the total amount of disorder.
The key observation is that ice melting is an endothermic process. If you think of the potential energy for the distance between water molecules, in the solid form the system is sitting right at the bottom of its potential well. In the liquid form, the molecules are futher apart, corresponding to an energy input - the latent heat of melting. Similarly the reverse process, freezing is exothermic - it releases energy.
Looking at the water molecules, when they freeze, the ice structure is indeed more ordered. And, correspondingly, the ice structure has a lower entropy than the free water molecules. But the energy that the freezing has released (eg into the surroundings) also has a corresponding entropy. Below 0°C, the increase in entropy in the surroundings created by all the new possibilities made possible by that released energy is greater than the loss of entropy caused by the increase in order of the water molecules that have frozen.
So, even though the water molecules that freeze become more ordered, and lose entropy, the system as a whole (the water molecules and their surroundings) increase in entropy, as by the 2nd Law they must, for the process to go forward. The water molecules lose entropy and become less disordered; but the system as a whole increases in entropy, and becomes more disordered. In each case, the direct equivalence beween entropy and disorder is upheld. -- Jheald 14:13, 25 June 2006 (UTC).

From the Nats article:

"When the Shannon entropy is written using a natural logarithm,

${\displaystyle H=-\sum _{i}p_{i}\ln p_{i}\,}$

it is implicitly giving a number measured in nats."

It should be noted that units so defined, that are 'implicit' (and this is not uncommon - there are many in the natural sciences) are artificial units. For the Shannon Entropy above, H, to have units as fundamental quanta of a physical characteristic of some system, the variable ${\displaystyle p_{i}}$ must itself have units. But ${\displaystyle p_{i}}$ is a probability, which is always unitless. A more obvious problem with the nat is that ${\displaystyle p_{i}}$ is the argument of a logarithm, and the arguments of operators cannot have physical units. Another example of this is the Boltzman factor: ${\displaystyle exp(Kb*T)}$ is not a physical quantity because the product of the Boltzman factor Kb and the temperature T gives units of Energy, Joules. You cannot take the exponent of something with units, just as you cannot take the log of something with units. You could artificially define the units of this quantity, but they are physically meaningless. Instead, what you see in physics is the quantity ${\displaystyle exp(Kb*T/hv)}$ where h is Planck's constant and v the frequency of photon emission of some physical system, the product of which is Energy, with units of Joules again. Now you have the exponent of an Energy over an Energy which is a unitless argument. The quantity now has a physical significance. The same situation is true for the Shannon Entropy. The nat is thus an artificial unit, and is therefore unphysical from the standpoint of fundamental physics. This is not to say it is not useful in some disciplines, (in particular signal processing).

Those who confuse the two should not feel bad. Confusing artificial, or constructed, units with physical units is common among non-scientists and even in first year physics classes I have to constantly encourage my students to watch their units so they do not carry quantities with units as the arguments of operators such as ln, log, exp, and so on. I remind them that only unitless quantities can be carried through these probabilistic quantities, and that in thermodynamics it is the Boltzman factor that properly scales statistical quantities. (In other words, the nat doesn't refer to anything physical i.e. "real" and you must therefore multiply it by the Boltzman factor to get a physical quantity). It should also be noted that it is quite common for idiosynchratic scientists and mathematicians to name often-used quantities for the ease of talking about them - and this happens with both physical and non-physical (i.e. probabilistic) quantities. I hope this helps give some perspective here. There are a lot of good discussions that can come from this Entropy article. As an instructor of physics for years, I have seen many of these arguments and I would enjoy discussing them all. Here is a great resource if you want to learn more! :)Cheers, Astrobayes 21:44, 23 June 2006 (UTC)

Huh? What you see all over the place in statistical physics is ${\displaystyle E/k_{B}T}$. That's an entropy in natural units. The typical units of Shannon entropy and typical units of thermodynamic entropy are entirely interchangeable. Nonsuch 04:10, 24 June 2006 (UTC)
${\displaystyle E/k_{B}*T}$ is exactly what I wrote above - if you read carefully you see that I say that the h*v quantity is exactly the E you're talking about and applies especially to thermodynamic systems such as blackbodies. As a scientist myself, I know what you "see all over the place" in thermodynamics. I am not speaking as a layperson here - I'm offering my official, professional expertise in this subject, to this article. And I'm trying to emphasize that what you're calling the thermodynamic entropy and the informational entropy are not the same (see the above reference peer-reviwed scientific journal article for proof). I can offer you many more examples. Astrobayes 19:43, 26 June 2006 (UTC)
Let me try and expand on what Nonsuch has written, and see if I can convince you, Astro.
Statistical thermodynamic entropy can defined (Gibbs) as
${\displaystyle S=-k_{B}\sum _{i}p_{i}\ln p_{i}\,}$
Entropy in information theory is defined (Shannon) as
${\displaystyle H=-\sum _{i}p_{i}\ln p_{i}\,}$
If the probabilities pi are the same, one can therefore write:
${\displaystyle S=k_{B}H\,}$.
Your instinctive complaint, I think, is that Boltzmann's constant is a quantity with physical dimensions, therefore to say that S and H are the same is to compare apples with oranges: physically they have different units, so must represent different things. Let me come back to that in more detail in a moment, but for now let me put it to you that since S = kB H, we can say at least that (if the probabilities are the same) H does give a measure of the statistical thermodynamical entropy S; just as in the article we say that S gives a measure of the energy unavailable to do work, TR S, even though S does not have the dimensions of energy.
Actually we can go further. Because of the First Law of Thermodynamics, we say that the thermodynamic entropy is conjugate to the temperature, S ↔ T:
${\displaystyle \mathrm {d} U=T\mathrm {d} S-p\mathrm {d} V\,}$
But equivalently one can write
${\displaystyle \mathrm {d} U=k_{B}T\mathrm {d} H-p\mathrm {d} V,\,}$
establishing that H is also a natural physical variable, one that is conjugate to kBT, H ↔ kBT.
Now you made the point that what is important are natural physical units, rather than artificial constructed units.
But what is the natural scale for temperature? The definition of the kelvin is pretty arbitrary. We happen to have chosen water to base our scale on, but we could have chosen the triple point of anything. What is more fundamental and much more physically significant is the corresponding energy kB T characteristic of a particular temperature. This energy, rather than bare T on its own, is what appears in equation after equation in physics.
The secret of choosing unit scales in physics is to choose the scales which make unnecessary constants of proportionality go away. We could choose units so that
${\displaystyle {\mathit {(Force)}}\propto {\mathit {(Mass)}}\times {\mathit {(Acceleration)}}}$
but instead we choose to measure force in Newtons, so that
${\displaystyle {\mathit {(Force)}}={\mathit {(Mass)}}\times {\mathit {(Acceleration)}}}$
Similarly, many physicists instead of a temperature in kelvins choose to always talk in terms of the characteristic energy at that temperature. (For example, the awesome Landau and Lifschitz "Course on Theoretical Physics"). Of all the scales we could choose for temperature, this (they are indicating) is the natural one, because it is the one that makes the constant of proportionality go away.
Now you are concerned that it is an arbitrary choice to measure H in nats (base e), rather than bits (base 2) or bans (base 10).
We have a free choice. We could measure information on the other scales. They would just introduce a multiplicative constant. The information entropy in bits is just 1.44 × the entropy in nats; or the entropy in bans is 0.434 × the entropy in nats.
But the nat (information) is the natural quantity to measure H in, because that is the one that, when we do the proof that statistical entropy reproduces the properties of Clausius's classical entropy, as done in the box here ("Entropy changes for systems in a canonical state"), is the choice that gives us
${\displaystyle \mathrm {d} H=\sum _{i}[d(E_{i}p_{i})-(dE_{i})p_{i}]/k_{B}T={\frac {\delta \langle q_{rev}\rangle }{k_{B}T}}\,}$
with no need for any unnecessary multiplicative constant.
Summary: H is just as much a physical concept as S. In fact, when you look at it, really it is actually the more physically natural variable for thermodynamic entropy. But in any case, a physicist should be able to move as readily between the uncertainty H and the conventional entropy S, as he/she does between the temperature T and the corresponding energy kB T. In both cases, they are just two different ways of describing the same physical thing. -- Jheald 09:10, 25 June 2006 (UTC).
I can appreciate the work you did for this argument but unfortunately, the peer-reviewed scientific literature does not support the hypothesis that " H is actually the more physically natural variable for thermodynamic entropy." (I provide a link to just such a study above where informational entropy and thermodynamic entropy are not only not the same, they can be antithetical). And this is exactly why I've started this discussion in this article. Since these are not the same quantities, and since the peer-reviewed scientific literature does not support that thermodynamic entropy and disorder are analagous, it is therefore a problem when individuals try to make predictions about thermodynamic systems (such as biological systems, the universe, or even engines) from an informational entropy understanding. Again, they are not the same. The peer-reviewed scientific literature does not support the assertion that they are. This is important, and I want to provide my expertise as a scientist, a professional, and furthermore - as a physicist - to improving the common misconceptions which are affecting the quality of this article. Cheers, Astrobayes 19:56, 26 June 2006 (UTC)

I took a quick look at the peer-reviewed article you mentioned, and frankly I'm not impressed. The author argues that in some cases the high entropy phase is what his intuition tells him is low disorder. (i.e. solid hard sphere fluid ant high density versus fluid hard sphere at the same density) But since he don't provide a quantitative measure of disorder (other than entropy) his intuition is irrelevant. And wrong. Nonsuch 22:19, 26 June 2006 (UTC)
Nonsuch, the point of the article was not to impress anyone. Such is never the point of any scientific endeavor. The point of science is instead to highlight that there exists a body of repeatable experimentation that shows the existence of a particular behavior and/or relationship between physical systems in the Universe. In this case, the peer-reviewed article (one of many) showed that thermodynamic entropy is not equivalent to disorder. In addition to my presentation of this reference (one of many if you get on Google Scholar) in this regard, it also bears the weight of a scientist author, a member of the scientific community with expertise in the subject matter discussed in the article. A refutation of the material presented in that peer-reviewed source can and should only be trusted if the refutation is itself published in a peer-reviewed source. Because you simply disagree with the peer-reviewed scientific conclusions presented in that professional journal article, it does not make the science go away. You are free to conjecture that the scientific conclusions are suspect, but they would not have passed peer-review if they were either irrelevant and/or wrong. By what qualifications are you making that judgement? In addition, if you are so impassioned, I encourage and recommend that you submit your own refutation to that very journal. They would, I'm sure, be happy to review your scientific work. So again, it's fine to disagree - but per Wiki standards, peer-reviewed journal articles definately count as verifiable sources whereas a particular non-specialist user's personal opinions do not count as verifiable sources. If I therefore make an edit based upon peer-reviewed research, and provide appropriate peer-reviewed citations for it, then by Wiki standards it should stand. And a revert by someone who personally disagrees would be more likely to be appealed. That is why I am sticking strictly to the science. I do hope in time I can clear up any misunderstandings you have and we can, together, improve the quality of this article... it needs it. Quality Wiki articles are my only desire here, I'm not out to do anything else. Cheers, Astrobayes 23:01, 26 June 2006 (UTC)

Paul, you made several semantic edits which change the context and tone of the article, but you added no citations for any of them. Your edits, if properly cited, could provide a valuable educational addition to the article. If not cited however, they seem an awful lot like POV. Astrobayes 20:24, 22 June 2006 (UTC)

Dear Astrobayes, if I cited Einstein, would that be his POV? I think a good article should at the very least consider feasible alternatives and not tout one POV. To consider what happens in an infinite universe, would be a sensible hedging of one's bets. Paul venter 22:12, 29 June 2006 (UTC)

## The second law does not apply?

At the bottom of the Overview section, it reads that the second law does not apply to the infinite Universe, yet further down the article in 'The Second Law' section, it reads that the entropy of the Universe does tend to increase. Maybe I'm missing something, but this may need clarifying in order to properly state whether or not the Second law applies to the universe or not.

Perhaps it was commenting on the fact that the second law states that entropy "tends to" increase - rather than always increases. Entropy doesn't always increase, it can decrease. However, the law states that in our humon observation, it usually increases. Fresheneesz 19:36, 29 June 2006 (UTC)
This is correct, and is in fact the crux of the entire concept of Entropy. Astrobayes 21:52, 29 June 2006 (UTC)

The jury is still out on whether the universe we live in, is finite in size or infinite. If it is infinite, the Second Law does not apply, if finite it would. Any statement about the entropy of "the Universe" increasing, is premature and speculative. My bets are with the infinite - you choose. Paul venter 21:28, 29 June 2006 (UTC)

## Entropy Sites

This article and Entropysimple.com are up for deletion. They merely contain 4 external links to web pages about entropy. I have added them to this article. If the regulars here like them, they can stay. If not they will go. The two articles concerned are most likely to be deleted and rightly so. --Bduke 01:07, 27 June 2006 (UTC)

• Delete from here also. Five links all going to one individual's sites is linkspam. If any of the links remain, they should carry a health warning. Contrary to the message these sites are pushing, it is misleading and unhelpful to claim that entropy relates only to the spreading out of energy. Also unhelpful is the jihad on these websites against the word "disorder". -- Jheald 01:36, 27 June 2006 (UTC).
Scientists are concerned with understanding the interactions between matter and energy in physical systems in the Universe, and quantifying these observations and understandings such that their conclusions are internally consistent, physically meaningful, testable, and reproducible. Your statement regarding religious connotations therefore does not apply. The reactions of scientists to clear up a broad misunderstanding by many people of a concept as important to the understanding of the physical world as is Entropy, is no different than the current efforts by scientists to clear up misconceptions that non-scientists have about stellar evolution, hot nucleosynthesis, evolution, particle physics, and so on. Perjoratives such as you use here are really inappropriate. We scientists are just doing our jobs to educate, and by that education to inspire and promote the love of knowledge. I would gladly discuss any science topic you wish by email at shale_d2010@yahoo, or on my talk page. Cheers, Astrobayes 19:55, 27 June 2006 (UTC)
Maybe. I'll look at them in more detail. I noted the comment from another chemist on the deletion page and I saw that the first one was by a retired academic. As a retired academic chemist who has taught physical chemistry, I may have an input. Give me a bit of time, and let us see what others think. --Bduke 02:08, 27 June 2006 (UTC)
• Delete all these links from here also (spam). Yevgeny Kats 05:00, 27 June 2006 (UTC)
• OK, I have looked at all four although not in complete detail. I agree that we should not include all four of them. I do not like the "Professor" v "Student" question and answer style in the 2nd and 3rd links (as the 4 are listed on the main page). However, they do contain material that is accessible to chemistry students, while the WP article is very much more what Physics students need. There is a need to add to the WP article some material which is more about entropy in chemical thermodynamics as presented in many textbooks on Physical Chemisty. I think it is also clear that the WP article is pretty technical and not easily accessible to the general reader. The author of these web sites has taught non-science students about entropy for many years. It is tough call and I think he does a pretty good job. I suggest we leave in the first link with a remark like "How an experienced educator taught entropy to non-science students". I think that would be helpfull to some readers. I would however welcome more comment before we act. Perhaps we should wait until the debate on deleting "Entropy Sites" is completed. --Bduke 06:00, 27 June 2006 (UTC)
• Delete I agree with the deletion of both of these articles, because Wikipedia should be an encyclopedia - but not an advertisement for a website, product, or person/entity. I have no problem with including these websites as additional links or references for this article on Entropy, and while they do attempt to present a truer picture of thermodynamics there are many, many peer-reviewed journal articles which carry more weight and which explore the same subject matter in more detail. So yes, get rid of the two articles. We can reference those websites here in this article - that use is completely appropriate. Cheers, Astrobayes 19:55, 27 June 2006 (UTC)

## Removed Confusing Text

I removed this text: "(Note that this is a simplification: entropy can relate to all kinds of multiplicity of possible microstates. However, with a bit of a stretch, almost all of that multiplicity can be considered as due to different possible energy distributions)." It was not only confusing as it was not attached to a particular reference or section, but the statements it made both before and after it's most recent edits were given no verifiable source to support it. It sounded an awfully lot like POV. If it were to be put back into the article, a verifiable source (by Wiki's standards) where that quote can be found should be included... and it should be placed in an appropriate section. A comment such as that which appears at the end of an article is quite odd. Astrobayes 22:43, 29 June 2006 (UTC)

The comment relates directly to the Lambert link.
If you want an example of the problem, consider the entropy of an alloy due to the mixed up arrangement of say copper and tin atoms. There are processes where you can actually measure that entropy per mole - it makes a physical difference. You can evade the issue up to a point, by saying that you're going to sweep in the different configurations as different vibrational energy configurations; but now think about the limit as you cool the system to absolute zero. There aren't any vibrational excitations any more -- but the entropy is still there; it doesn't disappear with some discontinuous step in the limit.
Statistical thermodynamic entropy is as a function of the probabilities of the states of the system as a whole; saying that it just relates to the energy is a sort of voodoo.
That is why several of the most recent textbooks, cited with a ** on entropysite, go out of their way to specifically flag up that distribution just of energy isn't quite the whole story. Jheald 23:45, 29 June 2006 (UTC).

Coming…The Full Monty on Disorder

Learning about Wikipedia and the power of the ‘users’ in the past few days is a Kafka-esque experience! In the real world of science – as with non-anonymous ‘users’ here – an author knows that his work will be read very critically by competent individuals before publication. (But I find that, not mentioned by any of you, the two ‘articles’ referring to my sites were submitted by a high school youngster! This is an amusing indication that I reach an audience of beginners over whose heads you shoot, but also a reason for its deletion. I would not have defended it for the five minutes I did – if I had known how to trace ‘users’ as page originators.)

A far more important shock is that an anonymous ‘user’ not only can misread and then can misrepresent my serious writing without any check with me prior to a public pronouncement. I’m referring specifically to Jheald’s off-base interpretation of four textbooks’ error as a challenge to my entropy approach (As I glance back, this is just the last of a host of other outworn, unacceptable to chemists nonsense that now really must be challenged – although all his points have been rejected by current chemistry texts or recent/coming journal articles).

Click on http://www.entropysite.com/#whatsnew , scroll to December 2005 and down to the texts listed as 11 through 13, and their common serious misstatement. Those texts tell students literally that “Matter tends to disperse”. Period. How does matter, how do molecules or atoms disperse? No association, no involvement with or dependence on molecular kinetic movement or consequently their ‘internal’ energy? That is prima facie ridiculous and a return to the era of phlogiston and alchemy. That is why I downgraded them as inadequate and not recommended. In contrast and in error, Jheald says [they, the texts/authors] “go out of their way to specifically flag up that distribution of energy isn’t ‘quite’ the whole story.” The ‘whole story’, Jheald and other ‘users’, is that those authors have screwed up! Matter can only disperse if molecular energy is involved. There's no 'quite' other whiffle dust causing it!

I’m surprised Jheald is surprised by mixtures (alloys as one type) having residual entropy at 0 K. Only a perfect crystal is defined as having 0 entropy there. I'd enjoy discussing private email-wise with Jheald (to save others from trivia) the solution to the classic residual entropy 'problem' substances, such as CO, FClO3 and water -- it is the existence of multiple Boltzmann-energy distributions that are frozen in at the equilibrium fusion point. (Journal of Chemical Education, by Evguenii Kozliak, publication in press, due out in 3-5 months.)

Ah me. I have now finally read over the whole W entropy chapter -- evidently strongly influenced by Jheald. I’ll have to write a “Full Monty” to demonstrate for you others, if not convince you of joining, the trend in all chemistry – including the latest to delete that sad old “entropy is disorder’”, Atkins’ worldwide best selling physical chemistry. Why should Wikipedia ‘Entropy’ be a relic of the 19th century? FrankLambert 19:25, 30 June 2006 (UTC)

To put my own POV on the table, I'm more in agreement with Jheald than you. I think you are doing untold (but hopefully minor)damage to the teaching of entropy with your jihad against the word 'disorder' and insistent on relating everything to energy dispersal. "dispersal" is no better (or less) defined than "disorder". And increase in entropy isn't all about energy either. Honestly, it is yourself who looks like they are stuck in the 20th (or 19th) centuries. (Out of interest, where do you stand on Launderer's principle? On the relation of thermodynamic and Shannon entropy?)
"it is the existence of multiple Boltzmann-energy distributions that are frozen in at the equilibrium fusion point.". O.K. that doesn't even begin to make any sense at all.
For everyone else, I would recommend this paper "Insight into entropy" by D.F. Styer, Am. J. Phys. 68 1090 (2000), which I just digested. It provides a much more balanced and nuanced discussion of the potential confusion of using the word "disorder" in explaining entropy. I rather like figs 2 and 3 which help demonstrate that we humans see patterns everywhere and are very bad at distinguishing true randomness. Nonsuch 20:17, 30 June 2006 (UTC) (A 21st century scientist.)

## Introduction

I hasten to thank you for discovering Styer (2000), and mentioning his conclusions to your W colleagues! Please glance at the start of my second paragraph in “Disorder…” and the first citation there: http://www.entropysite.com/cracked_crutch.html (He provided the physics support to me, and I used four of his illustrations. He later contacted me for backing him when Ohio was changing its HS exam requirements to include‘disorder’ in its question re entropy!) I disagree only with his suggestion of an additional ‘parameter’ for entropy: freedom. No way – students and we have suffered enough due to this kind of non-scientific obstacle (‘disorder') to understanding entropy!

I would also invite you to look at the seminal article of Harvey Leff, physicist and international authority on Maxwell’s demon) in Am. J. Phys. 1996, 64, 1261-1271. I discovered his paper only two days before I submitted the ms. for “Entropy Is Simple, Qualitatively” (that introduced the view of entropy change as a measure of energy dispersal rather than ‘disorder’: http://www.entropysite.com/entropy_is_simple/index.html ) Because of Leff's parallel views, I could smoothly and exactly cite points in his physics approach of “sharing and spreading of energy” to support the qualitative ideas of entropy change that I proposed and that have become accepted in chemistry textbooks. Finding that Leff and I live only ten minutes from each other, we have become scientific friends and associates. We are collaborating in a brief article for Nature. Last month he addressed a meeting of research physicists in San Diego on his spreading/ sharing concept of entropy change and a lengthy paper will be published in the report of that meeting in a few months.

You all would be well advised to read even Leff's 1996 article; it's an early statement of the physicist's counterpart to my low-level qualitative "entropy is a measure of the dispersal of motional molelcular energy" for chemistry.

Now to what I intended to use as an Introduction Thanks very much for your ref to reading that I had not known about, Wikipedia:Neutral _point_of_view. It certainly poses a double problem for me. You see, first, I am a Recovering Disordic, a RD. Just like an RA’s nerves are over-stimulated by only a whiff from the bar adjacent to a hotel lobby, the lengthy discussion in this Talk and the embedded disorder in the Entropy page unduly excite me. Second, I have an equally serious difficulty – but opposite, because it swamps me with serotonin: my POV that began and developed starting some eight years ago has become accepted dogma in chemistry. You in the entropy group seem not to understand that this has occurred. I am writing you about what WAS my POV and is now peer-accepted and in print. Here’s a brief of my sad story:

Never liking thermo, except for the power of the Gibbs free energy relationship, and never having to teach it, I was asked to develop a chem. course for non-science majors that would have more meaningful content and interest than any watered-down general chem. I came up with “Enfolding Entropy”, essentially a baby thermo course with minimal math. Marvelous fun for years. Good kids. In a very thorough ‘entropy via order-disorder’ that led to its (mis)application to human affairs in the last week or even two. I felt a bit uncomfortable. But not much. I put that aside because the students really could grasp why it required energy to produce hydrogen from water, and the problems in ammonia synthesis, etc.. etc.

After my second retirement, from a fascinating non-academic career, I had time to think. I began to wonder why Clausius’ q/T had begun to be applied to shuffled cards and, to start, I checked some history. Clausius, Boltzmann, Planck, and Gibbs , then Shannon and Jaynes – and things began to clear. I strongly advise it to each of you.

My first paper on shuffled cards as unrelated to entropy change caused the deletion of this silly example – my POV of 1999 is now the shared wisdom of all but one chemistry textbooks published since 2004 , whereas in 1999, it was the principal illustration of entropy increase in most general chemistry textbooks. In 2002, my POV discovery was that ‘disorder’ was a valiant try by Boltzmann but an untenable view because of his limitation to 1898 knowledge (prior to the Third Law, quantum mechanics, and full understanding of the energetic behavior of molecules).

As I have told you thrice, that seemingly personal POV of 2002 has, by 2006, resulted in the deletion of “entropy is related to disorder” from the great majority of new chemistry texts – including those in physical chemistry (although I can claim my direct influence only to two phys chems). This is perhaps an unprecedented rate of change in an ‘accepted’ concept in texts. It is not my famous name or power in the establishment that caused a total of 25 or so authors and hundreds of text reviewers to change their views! I am just the lucky guy who belled a giant cat that most chemist-authors had known was dead but wanted somebody else to say so.

My POV of 2002 that entropy is a measure of the dispersal of molecular motional energy has been equally well received and published in the texts mentioned in www.entropysite.com. It is no longer just MY "POV" !.

The newest developments are in the area of the coincidence of configurational entropy from classic statistical mechanics with energy dispersal: an article accepted for publication dealing with the residual entropy of CO, etc., one (in the second round of review) urging the deletion of ‘positional entropy’ from general chemistry, allowing emphasis only on ‘thermal’ entropy, and an article (Hanson, J.Chem. Educ.,83, 2006, 581. April issue. Check eq. 2 and 5, and read the quietly explosive conclusions beneath eq. 5. And Hanson had opposed me from the start in 2002!). My colleague, E. Kozliak at the University of N. Dakota has a fundamental theo paper in preparation showing why and when configurational entropy coincides with results from energy dispersal views.

## The Full Monty

### Disorder

Boltzmann was brilliant, probably a genius, far ahead of his time in theory but not flawless and, most important for us moderns to realize, still very limited by the science of his era. (Some interesting but minor details that are not too widely known: Even though he died in 1906, there is no evidence that he ever saw, and thus certainly never calculated entropy values via Planck’s 1900 equation, S= R/N ln W [in an article but not printed in a book until 1906, as] S = kB ln W , that is carved on Boltzmann’s tomb. Planck’s nobility in allowing R/N to be called ‘Boltzmann’s constant’, kB, was uncharacteristic of most scientists of that day, as well as now!)

The important question is “what are the bases for Boltzmann’s introduction of order to disorder as a key to understanding spontaneous entropy change?” That 1898 idea came from two to three pages of a conceptual description, a common language summary, that follow over 400 pages of detailed theory in Brush’s translation of Boltzmann’s 1896-1898 “Lectures in Gas Theory” (U. of California Press, 1964). The key paragraph should be quoted in full – preceding and following phrases and sentences primarily repeat or support it (disappointingly) without important technical or essential additional details:

“In order to explain the fact that the calculations based on this assumption correspond to actually observable processes, one must assume that an enormously complicated mechanical system represents a good picture of the world, and that all or at least most of the parts of it surrounding us are initially in a very ordered – and therefore very improbable – state. When this is the case, then whenever two of more small parts of it come into interaction with each other the system formed by these parts is also initially in an ordered state and when left to itself it rapidly proceeds to the disordered most probable state.” (Final paragraph of #87, p. 443.)

That slight, innocent paragraph of a sincere man -- but before modern understanding of q(rev)/T via knowledge of the details of molecular behavior, quantum mechanics, or the Third Law – that paragraph and its similar nearby words are the foundation of all dependence on “entropy is a measure of disorder”. To it, you and uncounted thousands of others owe the endless hours you have spent in thought and argument. Never having read it, you believed that somewhere there was some profound base. Somewhere. There isn’t. B. was the source and no one challenged him. His words have just been accepted for a century. There is NO scientific basis for seeing entropy as involving order and disorder. Boltzmann’s conclusion was fallacious due to his primitive concept of “increased randomness” in a system at equilibrium (that we now recognize as a maximal number of accessible quantum states under the system’s constraints) naively coupled, because it is an even more primitive idea: there must be an opposite, namely, if the final state is disordered, the initial state must be ordered.

To the contrary, scientifically. If the final state has additional accessible quantum microstatesnot to be confused by those of you who flip back and forth from stat mech locations in phase space that you call microstates – then the initial state merely has fewer accessible quantum microstates. The most obvious example, that was so often mistakenly used in elementary chemistry texts prior to my corrections is ice melting to water. Sparkling orderly crystalline ice to disorderly mobile liquid water. That’s the visual and that’s the crystallographic conclusion, but it is not the conclusion from entropy calculations.

The So for liquid water at 273 K = 63.34 J/K mole. Thus, via S = kB ln W = 10 to an exponent of 1,991,000,000,000,000,000,0000,000 (qm microstates). But for crystalline ice at 273 K with an So of 41.34 J/K mol, S = 10 ^ 1,299,000,000,000,000,000,000,000. This shows that ice is “orderly” compared to liquid water? Of course not. Ice simply has fewer accessible quantum microstates. And that is the universal modern criterion.

Gibbs “mixed-upness” is totally irrelevant to ‘order-disorder’ or any other discussion. It comes from a posthumous fragment of writing, unconnected with any detailed argument or supporting any concept proposed by Gibbs.

• Jheald has revised a paragraph in the article, and wrote "Increases in entropy can in fact often be associated with apparent increases in order at a macroscopic level, if these are accompanied at the same time by an increased dispersal of energy". It would really help if he gave an example to the first part of the sentence, and also it's necessary to define the term "dispersal" which he uses in the second part of the sentence. Otherwise I have no idea what he is talking about (even though I know what entropy is). Yevgeny Kats 15:36, 2 July 2006 (UTC)
Yevgeny, I was trying to acknowledge some of the (legitimate) concerns that people do have about the word "disorder" for entropy. In particular, for many processes although the total entropy increases, when you look only at the most visible aspect of the system, that aspect appears to become more ordered. For example, a lump of ice growing in freezing cold water below 0 deg C; or a protein chain being synthesised in a cell. It's only when you consider the latent heat being released by the ice forming, or the free energy released by the ATP -> ADP + Pi reaction which powers the protein synthesis, that it becomes appropriate to say that the system as a whole is indeed becoming more mixed-up or disordered.
I didn't want to spend too many words in the article on what entropy (or disorder or mixedupness) isn't, at a point before we've even started to discuss how to think about what entropy is. I was afraid that expanding into much more detail would actually unbalance the complete shape of the overview.
But I meant the text I edited in only as quite a tentative suggestion, for discussion and accepting/rejecting/re-editing or wholesale rewriting. If you look at the immediate edit diff, IMO it's a more accurate than the text that was previously there by Freshneez, and better fits with the rest of the article as it is at the moment. But as I said, it was just a suggestion, and I'm entirely happy for anyone else to have a go.
This only means that one should be aware not to look only at the most visible aspect of the system but also consider the increased disorder of the water and the rest of the environment when the lump of ice is formed (related to the fact that the environment heats up). So overall, I don't see how this example disagrees with the statement that entropy is correlated with disorder (and I think Jheald, but maybe not Frank, agrees with me on that). I still find it misleading to use the vague word dispersal instead of talking about the increase in the disorder of the environment. (I agree, by the way, that the previous formulation of that paragraph was worse.) Yevgeny Kats 21:47, 2 July 2006 (UTC)

### Thermodynamic entropy

Aware of the thinking of Lazar Carnot and Kelvin, among others, Clausius enormously increased the power and applicability of their general idea of heat becoming dissipated in a process by including the essential factor of the temperature at which the energy dissipation/dispersal or spreading out occurred via dS = dq (rev)/T. Thermodynamic entropy cannot ever be separated from energy being ‘transformed’ (as Clausius viewed it) or somehow dispersed (in modern words) divided by T.

Even though Joule, Kelvin, Clausius and Maxwell thought about thermodynamics in terms of molecular motion, lacking knowledge of molecules other than bits such as velocity and mean free paths, Clausius’ conclusions could only be framed in/from macro parameters. The detailed nature of what was occurring in dq as a general symbol for a change in the internal energy of a system, was ignored for a century because of the remarkable success of classical statistical mechanics in predicting the magnitude of entropy change in many processes.

For example, such spontaneous events as gas expansion into a vacuum or mixing of gases or liquids, could only be treated by Clausian entropy by finding the quantity of work required to restore the system to its initial state (equaling –q for the forward process). In contrast, by allocating ‘cells’ or ‘microstates of location in phase space’ for molecules or all possible combinations of several molecules , statistical mechanical combinatorial methods could directly count and predict the entropy change in a forward process of expansion or mixing.

It appeared that, because only the number of locations of cells were being counted (and the temperature was unchanged), this ‘configurational or positional’ entropy was unrelated to Clausian ‘thermal entropy’ and apparently did not involve molecular energy. In any equation, the initial energy was unchanged and thus dropped out of the Sackur-Tetrode or ln WFinal/WInitial equations. But conceptually, there is an obvious error – the initial motional energy of the molecules in an expansion or in forming a mixture with another components’ molecules is becoming more spread out in a three-dimensional volume and more dispersed in changing to a new equilibrium. (This is precisely what happens to the energy of a hotter surroundings plus a cooler system. The initial total energy of system plus surroundings is not changed, but some motional energy of the hotter surroundings’ molecules has become spread out to those in the cooler system to raise it to some temperature that is an equilibrium of the universe of surroundings and system.)

The cause of the error also becomes obvious, once stated quantitatively: in phase space a cell ‘location in space’ is also its ‘energy in that space’ and thus any combinatorial measure of increased number of locations for a gas expanding to fill a greater volume is exactly the increased number for the dispersal of the initial motional energy of that gas. Both configurational entropy and thermal entropy measure what Clausius and Kelvin and Carnot tried to express with macro parameters for spontaneous processes – defined in modern terms as “changes occur in systems to yield an equilibrium wherein the motional energy of the molecules in a system is maximally dispersed at the final temperature in the sense of having the maximal number of accessible quantum microstates for the system’s energy at that temperature". (bad long sentence. good concept.)

I once wrote “…violently energetic, speeding gas molecules will spontaneously move into an evacuated chamber or mix with another gas…summarized as increases in entropy” Oberlin thermodynamicist, Norman Craig corrected me: “…in saying that, you are ‘smuggling in’ entropy. Movement of molecules does not cause an entropy increase even though [it] enables an entropy increase.”

He is right. Two factors are necessary for thermodynamic entropy change. An increase in thermodynamic entropy is enabled in chemistry by the motional energy of molecules (that, in chemical reactions, can arise from bond energy change). However, entropy increase is only actualized if the process makes available a larger number of arrangements for the system’s motional energy, a greater probability of an increased distribution for the system’s energy.

The two factors, energy and probability, are both necessary for thermodynamic entropy change but neither is sufficient alone.

From this it can be seen the ‘configurational or positional’ entropy – when thought to be only as ‘a measure of the probability of locations’ is a smuggling-in of thermodynamic entropy – the essential enabling factor that makes actual physical/chemical change in matter possible and not just an exercise on paper or computer screen is missing. A student -- or an experienced person - as you all demonstrate -- can be misled and think of it as 'just due to arrangements in space'.

### Information “entropy”

The misnomer of “entropy” should always be in quotation marks if the subject of thermodynamic entropy is present in the same article. The reason is clear (as stated above and repeated here):

Two factors are necessary for thermodynamic entropy change. An increase in thermodynamic entropy is enabled in chemistry by the motional energy of molecules (that, in chemical reactions, can arise from bond energy change). However, entropy increase is only actualized if the process makes available a larger number of arrangements for the system’s motional energy, a greater probability of an increased distribution for the system’s energy.

The two factors, energy and probability, are both necessary for thermodynamic entropy change but neither is sufficient alone.
In sharp contrast, information ‘entropy’ depends only on -k Σ[Pi log Pi], where k is an arbitrary constant that never is required to involve energy, as does kB. However, merely substituting kB for k does not magically alter a probability of shuffled cards or tossed coins to become a thermodynamic entropy change! A system must inherently, integrally possess energy transfer entities such as moving molecules.
(‘Sigma entropy’ in physics, σ = S/kB, depends only on the one factor of probability. Fine for physicists, I presume. Misleading for chemistry students.

Landauer? Check his "Minimal Energy Requirement IN COMMUNICATION" Science,272, 1996, 1914-1918. I'll ask Leff about this next week, but I am only concerned about thermodynamic entropy and, as stated above, the gulf between thermo entropy and info "entropy" is absolute and unbridgeable. von Neunamm has robbed you all of weeks of your lives or even more. Some cruel joke, that. FrankLambert 21:32, 1 July 2006 (UTC)

I'm familiar with this paper, yet another classic by Landauer. From the abstract, "Alternative communication methods are proposed to show that there is no unavoidable minimal energy requirement per transmitted bit." You don't need to expend any energy to move bits around. But I fail to see what this has to do with the discussion at hand. Nonsuch 04:20, 2 July 2006 (UTC)
Your last paragraph final gets to the heart of the issue. My POV is very different. Modern statistical physics and information theory forces us to acknowledge that there is no fundamental difference between thermodynamic and Shannon entropy. A bit is a bit, whether it is encoded by a macroscopic object like a coin, or a mesoscopic object such as a collection of transitions, or a single microscopic molecule (With the caveat that if quantum effects are important I need to talk about qubits). If this were not the case then we could construct Maxwell demons and circumvent the 2nd law. In the modern view, the relation \int dq_rev/T is a method of measuring entropy under certain conditions, not an irreducible definition of entropy itself.
Now, admittably, you're not the only person with your general point of view, but then I'm not alone either. (And I'm right, or at least less wrong ;-) ) Ideally, we should incorporate this difference of opinion into the article. Nonsuch 04:20, 2 July 2006 (UTC)
I challenged Nonsuch, as I do any of you, to cite any textbook in chemistry that says any such thing as "there is no fundamental difference between thermodynamic and Shannon entropy". I have seen no chem text that agrees with him. No chemistry prof in thermodynamics that I know, and my acquaintance is wide, shares that view. Those to whom I mentioned it years ago barely let me say it before looking at me disdain with a 'fgeddaboudit'. BUT I want to know the data -- about CHEMISTRY texts/ authors. They're the ones who have to teach entropy to the most students!

I have challenged Nonsuch, and urge others, to tell me what modern (2004 and after) university chemistry textbooks, including physical chemistry (the text that most emphasizes physics) (but excluding biochem; they have to be sloppy) still use 'disorder' in introducing entropy to students. The question is important because (1) it is not my POV; it's objective data re the deletion of 'disorder'as related to entropy in chemistry instruction. (2) entropy and the second law are far more central in beginning chemistry than in beginning physics. (Compare the pages devoted to each for the second law, entropy concept(s) and calculations, and use of the Gibbs free energy relationship with calculations.)

Although you and I were thoroughly taught that "entropy increase is 'disorder' increase", after learning of its origin in Boltzmann's innocent but unscientific statement from 1898, we can be free. The revolution in chemistry texts is real, objective, here now. A modern encyclopedia should certainly be as modern as elementary instruction about a topic! What other goal? Obsolete stuff? "Energy dispersal"? Kats (and others) perhaps have not read my description of entropy change as simply what lies behind the basic dq/T -- it represents the dispersal/spreading out of the motional energy of molecules (heat, to Clausius) to a greater volume of space/T (whether heating [surr.+ sys. always], gas expansion, fluid mixing, i.e. all types presented to beginners). That is inital and superficial BUT it can be readily communicated even to 'concrete-minded' students [or Wikipedia readers] almost instantly because, in chem, they have been told about fast-moving molecules (hey, they're going a thousand miles an hour on average at ordinary temps, five times faster than NASCARs, and continually colliding with each other, etc., etc.) But then, the advantage of this low-level approach is that it can seamlessly lead to the next level, scientifically.

The introduction of quantization of all energies, molecular energies on quant. levels specifically (simple QM deductions: more energies spread out on higher B-distribution levels in hotter systems, denser energy levels in systems with increased volume, etc.), the idea of QM microstates (NOT 'cell-model' stat mech 'microstates'!), and that an increase in entropy is related to a greater number of accessible QM microstates -- what Leff calls "temporal spreading of energy"; more choices of a different microstate at the next instant in time.

Compare that to the crap of 'disorder'. If you stick with 'disorder', you deserve the reward of being mired, don't you? :-) FrankLambert 06:19, 3 July 2006 (UTC)

I understand here that by "energy dispersal" Frank sometimes refers to heating [surr.+sys.], sometimes to an increase in volume, and sometimes to fluid mixing. It seems like for every type of a physical process he would need to define separately what "energy dispersal" means. Then I would say that this concept is pretty useless. Yevgeny Kats 03:34, 4 July 2006 (UTC)
I think that you really, 'implicitly', know how molecular energy is dispersed in each case, but thanks for the chance to show everyone the immense power of this simple approach,Yevgeny. (Check Leff's seminal paper about the spreading and sharing of energy from a physicist's viewpoint spatially and temporally.) Recall your first year intro to kinetic molecular theory -- the diagram of molec. movement at various temps of O2/N2, etc. (And, obviously, similar speeds in liquids and similar energy in librational movement in solids at the same temp.) As I repeated so many times to this group, and which is a major point to the 'concrete-thinking' individual whether student or adult, those speeding molecules can be likened to thousand mile an hour vehicles, constantly violently colliding, but bounding off one another with no energy loss. Obviously easy to 'sell' visually in a lecture or a text or an encyclopedia. Then, recall the stereotypical Figure of a two-bulb setup connected with a tube with a stopcock: one bulb with bromine vapor, the other evacuated. When the stopcock is opened ['that constraint on the system removed'], of course the listener/reader him/herself foresees that those amazingly fast, colliding particles will 'explore' the new additional volume.
But what is happening energetically? Is the initial motional energy changing? (Ideal gas; isothermal conditions.) No way! That energy is simply becoming spread out, dispersed over a larger volume. (That's the first factor in entropy change, enablement of a process by molecular energetic movement. Probably for the majority of any population, this is enough. Yes, it is 'smuggling-in' entropy change, but the second factor -- going into quantized energy details -- is difficult for 'concrete-thinkers'even though it is a smooth transition for chem/physics majors.) Conclusion, therefore: the energy inherent in molecules that are moving spontaneously disperses or spreads out spatially. That alone is key to gas expansion, to mixing of one volume of one fluid with volume(s) of another fluid or of dissolving an ideal solid solute in a liquid -- all the usual treated by stat mechanics, not involving 'thermal energy' transfer.
In a 'dispersal of energy' approach, the second factor in thermodynamic entropy change is the effect of a process on the quantized distribution of molecular energy. Here is where students (or W readers in a special section?) are introduced to quantized energy levels for molec. energy, the effect of volume change on distance between levels, the meaning of a QM microstate as one arrangement of molec energies at one instant, the Boltzmann relationship of S and ln W, and that an increase in accessible microstates is what one means QM-wise in saying "energy dispersal" -- e.g., the system is involved in an energetic temporal dance, instant by instant, over a very large number of possible states (but a relatively small fraction of possible Ws in an eon, i.e., quasi-ergodicity.)
The strength and attractiveness of the approach are that it also includes all that is normally considered as energy change due to heating. When considering a situation that involves heating a system, obviously treatable by the Clausius relationship, you probably never think of it as involving spatial dispersion of energy. (At least I never had before exploring the implications of energy dispersal.) However, that is a mindset that is drilled in us by our focus in discovering the solution to our first such problem -- similar to a magician fooling us by distracting our attention. Whether the traditional first physics example of a slightly warmer metal brought into contact with a slightly cooler metal, or the chemistry stereotype of melting an ice cube in a warmer room, the final result is that the combination of units, metal plus metal or system plus surroundings have undergone a greater dispersal of total energy spatially.
Remember the convoluted back and forth you had on the illustration of ice and water. To an (admittedly superficial) 'concrete-thinking' student or adult presented with the basic idea that energy simply spreads out in space, that example would be no reason for any back and forth at all. The warmer room has more concentrated thermal energy than the glass and contents ; the energy disperses throughout both -- no matter how large is the room or how small the glass of ice and water, that original energy has become more spread out. (And that could open a discussion of equilibrium as a state of maximal entropy.) Of course, that is over-simplified even for most classes or readers, but it illustrates how broadly a view of spatial dispersal of energy is both applicable and correct. No big deal need for special something or other in every situation that Kats implies.
Of course, the warm room, glass of ice in water case should be developed in more depth in any classroom and at least in a box insert in Wik. Here is where the idea of always considering system plus surroundings must be introduced, that a spontaneous dispersal of motional energy from one to the other only occurs because/if there is a greater increase in the distribution of energy in the recipient than than the decrease in the donor. And, although another superficial aspect of such energy transfer is always from a higher temperature component to that which is at a lower temperature, the fundamental reason for the energy to be more dispersed in the lower temperature entity is an increase in the occupancy of higher molecular energy levels that is greater than the decrease in occupancy of energy levels in the donor entity. (Consequently, there is a greater increase in the number of additional accessible microstates there than the decrease in accessible microstates in the high temperature component.) Enabled by motional molecular energy...actualized by the process (here, as in gas expansion, a spatial spreading out of motional energy, but unlike isothermal gas expansion where motional energy levels become more dense, thermal energy transfer involves a greater occupancy of higher energy levels in the recipient system or surroundings.)
Contrary to Kats, this is a surprisingly powerful and useful concept, with an across-the-spectrum application from naive student or Wik reader to -- evidently -- graduate students in physics. FrankLambert 13:09, 4 July 2006 (UTC)

Frank, you are deliberately confusing two issues. One is, is it useful to describe entropy as disorder to undergraduate chemists? (Possible not, although I'm not convinced.) The second is, is entropy a measure of disorder? (To the extent that disorder has a quantifiable meaning at all, then yes.) Your assertion about textbooks supports the first issue, but is irrelvant to the second, despite your apparent inability to grasp the concept yourself. Nonsuch 04:44, 4 July 2006 (UTC)
Disorder has been a failure in describing entropy for a century. Your acre of discussion here on these talk pages is perfect support for that conclusion, but only an inkling of its vagueness, non-scientific 'quantization' and failings. That really takes care of your 'second objection' but please go to the end of "A Quantitative question..." below. Can you, with a straight face, tell someone that difference in all the knowedge in the world in 2004 is ordered whereas all the knowledge in the world in 2005 represents disorder? Entropy is NOT a measure of disorder -- that's utter nonsense. The only quantification is in numbers of microstates and why take the trouble to wave your arms about disorder before you go to the numbers?!
I'd feel entirely happy that a macroscopic description which left "all the knowedge in the world in 2004" of uncertainty could be described as having that much mixedupness; and that one which leaves "all the knowedge in the world in 2005" of uncertainty defines that much more mixedupness. Jheald 22:07, 4 July 2006 (UTC).
Now as to your first point for ALL chemists and scientists dealing with entropy....Go to any gathering of alums, ask your friends who aren't as bright as you, stand outside a classroom after the thermo chapter is over -- ask them "Do you understand entropy? What is it, really?" Nonsuch, I've talked with students, I've talked with profs, I've read the results of research in 'understanding of entropy concepts' in Turkey and the UK -- they're all the same. In general, students can parrot "entropy is disorder" and that's it. Ask them what this means, and the result reported is a blank stare or a repetition in a blank of a survey. The responses I have received -- unsolicited of course!!!-- from beginners to grad students is, "I never understood this stuff until I read your site". FrankLambert 13:37, 4 July 2006 (UTC)
One of frank's point is that "mixedupedness" and "disorder" is shit for terminology and was used to describe it to "laymen" - who apparently learn better if you lie to them. However, I believe this point has already been addressed, and the article in fact already discourages the use of such terms. Fresheneesz 08:43, 5 July 2006 (UTC)
I was wrong, this article keeps putting in crap about disorder. Its a horrible horrible concept. Also, note that the second law of thermodynamics states a generality - not a rule that hold all the time everywhere. So Entropy *can* decrease, it simply can. No increase must occur elsewhere and the law would still hold. However, this situtation does not happen often at all. Fresheneesz 08:53, 5 July 2006 (UTC)

## Appeals to Authority

Since the debate on Entropy and Disorder isn't really going anywhere, I thought I would try a different tack, and make abject appeals to authority. (Not my favorite approach.) Frank's appeal to authority is that recent physical chemistry textbooks use the term "disorder" far less than they used to. I find this unconvincing since introductory physical chemistry textbooks really suck at explaining the deeper principles. (I curse Atkins to this day.) In response, let me quote Callen, arguable one of the finest books on thermodynamics yet written:

"Thus we recognizer that the physical interpretation of the entropy is that the entropy is the quantitative measure of the disorder in the relevant distribution of the system over its permissible microstates"

Or how about Feynman's Lectures in Physics, another very good book :

"We measure 'disorder' by the number of wasy that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the 'disorder' is less."

Or "Thermal Physics" by Finn, another good, modern thermodynamics textbooks.

"It is usual to identify [entropy] as a measure of 'disorder' in the system. This implies that we expect the disorder of an isolated system to increase."

Whatever. Nonsuch 00:51, 6 July 2006 (UTC)

I don't think we should be looking at useage of the term in physics or chem books. One reason being that those books don't usually explicitely condone or condemn the term or concept - they just use it. Thus its basically original research to use that argument. However, anyone that understands entropy will tell you that terms like "disorder" and "mixedupedness" are failing at teaching our children the important concept of entropy that has its base in heat and statistics - *not* "order", whatever that is. Fresheneesz 04:21, 7 July 2006 (UTC)

## Authority, Shmathority!!

Nonsuch, first put in your contacts so you can read what you wrote, a powerful support for one principle that I have been pleading for: 'disorder' is a dead obstacle between entropy and a measure of the number of microstates in a system. Look:

Old Callen (1985) wisely said (you tell me): "...entropy is the quant. measure of...the relevant distribution of the sys. over its permissible microstates".

And even Feynman gets it right sometimes (!!) in his famous quotation: The logarithm of that number of ways [the number of ways that the insides can be arranged, so that from the outside it looks the same] is the entropy."

How many times have I told that to Jheal, the information "entropy" maven who is working the wrong side of the street from his day job at the 'Information "entropy" Wiki page! I'm not arguing from authority, I'm arguing from history -- you guys never read that lead paragraph of Boltzmann's that was the tiny, non-scientific cause of the whole mess for a hundred years. You're bound up in your obeisance to unsubstantiated dogma that was given you by people you respect, but who were as uncritical of what THEY were taught as you. I'm arguing from success: with 'disorder' dead -- and you're the hapless rear guard in its defense, just as all 19th century leaders had to die before the ideas of younger people were accepted (tetrahedral carbon, Boltzmann's theory, etc., etc., etc. -- with gone, what is the replacement?

You forget that you are writing for a wide range of backgrounds and abilities in Wikipedia about thermodynamic entropy. FIRST, should come the simple presentation, from which you build to the more sophisticated view of quantized energy states and then microstates. Only fourth, fifth or tenth should you hint about other interpretations of entropy and refer to your details in info "entropy".

As I've told you, and repeat (because you continue to lose your contacts), should come the simple examples of the second law, spontaneous events, THEN go to what's happening on the molecular level (Tell 'em about those incredibly speeding banging molecules. Hey this is chemistry in thermodynamics, not exclusively physics!)apply that to gas expansion into a vac, the old two bulb deal, then perhaps food dye in water or cream in coffee. Molec. motional energy disperses!

Only then begin to develop energetics, microstates, etc....for the boffo climax that we all know about -- THIS is what entropy IS FrankLambert 14:59, 6 July 2006 (UTC)

FL, please limit the personal attacks. My eyesight is just fine. I have been trying to lead you into an informed, scientific debate. I would honestly like to understand your POV (Which is different proposition than agreeing with it.) But instead you keep responding with the same vapid verbiage. I'm finding it hard to understood what exactly you think the problem is with equating informational and thermodynamic entropy***, apart from a dislike of the descriptive work 'disorder'.
***Informational "entropy" has no integral/required/internal energetic material component and no interest in energy transfer per se. This is in stark contrast to thermodynamic entropy that has meaning only in in the measurable changes in properties of systems of matter and energy. 'Thermo dynamics' -- the name entails what 'informational' does not.
Sorry, but I have spent so many hours in patient detailed explanations to you 'Wikipediatrics' with little apparent understanding on your part of a relatively obvious approach to entropy. In my contacts with professors who teach as well as resarch, there is an incomparably higher percentage of understanding (and acceptance) than among you -- although, astonishingly, there are only 3 or 5 'alive' individuals here. I wonder how creative, how rebellious, how open you were/are to tossing a whole lot of experimental work out, and turning to find a better way than that which you had been pursuing. Certainly, none of you have done more than a year or two teaching beginners and had to think of creative ways to reach them. Perhaps that is the problem -- you haven't been in the trenches enough to know the battle that goes on down there with naive individuals, many of whom aren't too excited about dealing with abstractions!
I greatly appreciate your example. (I don't hate the system -- I hated textbook authors who misled young readers!) I'll insert asterisks after each question, for easier connection -- without breaking up your paragraph.FrankLambert 05:50, 7 July 2006 (UTC)
So lets try a specific example. I hand you a shuffled deck of 52 playing cards. (This is one system that you clearly hate, so you should be able to articulate what the problem is.) The cards are disordered, by any reasonable definition of the word disorder. Would you agree that the Shannon information entropy is log_2 52! = 225 bits and change?*1 All configurations have the same energy, for all intents and purposes.*2 (These are idealized cards, natch.) O.K., now I hand you a shuffled deck. Can you sort them into a predefined order?*3 This will reduce the Shannon entropy to zero.*4 Can you construct a mechanical device to sort many decks into the same order? I'll also give you two heat baths at different temperatures, so you can construct a heat engine. Can your mechanical device sort a deck without altering the rest of the universe?*5 If you must change the universe, then what is the average minimum change per deck?*6 In particular, what is the minimum amount of energy that you would have to pump between the heat baths to sort the cards?*7 What is the corresponding entropy change of the heat baths?*8 Would anything change, fundamentally, if I were to use 52 different molecules?*9 (E.g. DNA triplets?)
• 1, fine. *2, yes AND each the same entropy (Std. thermo entropy at 298 K of 84g. (wt. of a deck)/avg MW of a mole of cellulose.) of the g.cellulose/Mol. wt. cell. *3, sure, but no change in deck's thermo entropy. *4, sure, showing the irrelevance to thermo entropy. *5, no, it could not sort nor idle, doing no work, without changing the entropy of the univers. *6, impossible to calculate (for me, maybe a good thermodynamicist could) thermodynamically but totally of no consequence thermodynamically because the thermodynamic entropy of the cards is not changed in any configuration. The Landauer answer that you will give shows why informational "entropy" MUST have quotation marks around it -- it is no way related to thermodynamic entropy because the cards have no internal inherent energy to enable them to change dynamically from one configuration to another (as do assemblies of ideal molecules). *7, same as 6. *8, same as 6. *9, hell yes! Now you're in the field of thermodynamics -- although not of entropy because there are too few particles to assure a totally random distribution of their motional energy;..you'll have important energetic attractions that assure certain configurations will be present in a final/semi-final state. You can can have a lot of fun attaching your 'important information states' to actual important bond-formed states (which are actually due to -- wonder of wonders -- the fact that energy is more readily dispersed to the solvent/surroundings when such bonds are formed :-) FrankLambert 05:50, 7 July 2006 (UTC)

This chain of logic isn't original or particularly recent. No one at the frontier is being unduly influenced by what Boltzmann may have said a 100 odd years ago. Nonsuch 16:52, 6 July 2006 (UTC)
Sorry you just don't understand -- throughout your scientific life (and those who have lived through the last century), you have been embedded in a system in which 'disorder' was the only way to look at entropy. You had no choice, your prof had no choice, you had no reason to rebel -- if you, as too many scientists are, conformist when they think it doesn't matter. It may not, to you and other pros but I know from talking with students, hundreds of emails from them, from profs who are authors that it does matter to beginners. It helps to a logical way of viewing entropy.FrankLambert 05:50, 7 July 2006 (UTC)

Nunsuch you say,"I'm finding it hard to understood what exactly you think the problem is with equating informational and thermodynamic entropy..." The problem with equating these is that doing so leads to results that are nonphysical and in fact, the peer-reviewed scientific literature is full of research showing that Entropy and disorder are in fact anti-correlated. So, unless we want to ignore peer-reviewed research, we need to concede - in this article - that it is non-physical to call Entropy "disorder" all of the time. I have followed this talk page debate for some time, and in none of the statements you have made have you supported them with any peer-reviewed research - you've only used old textbooks and anecdotes of scientists giving public lectures about this topic. Unfortunately, this subject is often so diluted when presented to the public that the real physics gets glossed over in favor of a palatable description for non-scientists. Well I feel it is possible to present Entropy the way it is without diluting it. As I've said before, we know now that it is incorrect to view the atom from the Bohr perspective. Only elementary school children are taught such things. Teaching Entropy as disorder is like stating that the atom behaves as in the Bohr model. It's not a matter of not liking it - it's just wrong as far as physics is concerned. Entropy and informational "disorder" can not be equated as a general rule. By the way, Nonsuch, what is your educational background? I may be able to help clear up some of your misunderstandings on this topic if I understand what educational perspective you're coming from. Cheers, Astrobayes 20:42, 6 July 2006 (UTC)
"The problem with equating these is that doing so leads to results that are nonphysical and in fact, the peer-reviewed scientific literature is full of research showing that Entropy and disorder are in fact anti-correlated." What? Where? Citations please. "anecdotes of scientists giving public lectures about this topic" Now you are making stuff up. The quotes where taken from some of the finest science textbooks ever written to show that some very smart people, who thought very deeply about thermodynamics, thought "disorder" was a reasonable word to use when explaining what entropy really is.
The Bohr model analog that you're parroting is backwards. Pretending that informational and thermodynamic entropies aren't related is to pretend the last 50 odd years of research into the physics of information didn't happen. Go on, explain what you think the problem is with the card unshuffling example? Or do you think that you can sort a deck of cards for free? Or perhaps a shuffled deck isn't disordered? Once more the inescapable consequence of Landauer's principle is that either information and thermodynamic entropy are related, or the 2nd law doesn't hold. More references? The book, "Complexity, Entropy and the Physics of Information" edited by W.H. Zurek is a good resource.
I rather argue facts than authority, but for what it's worth I'm a professional scientist (Piled Higher and Deeper) with a broad background in thermodynamics and information theory. I know of which I speak. Nonsuch 21:44, 6 July 2006 (UTC)
Astro, let me add that he didn't ask you what your problem was with "informational disorder". He asked you what your problem was with equating thermodynamic and informational entropy.
Sure, there are cases where the word "disorder" can be confusing, if it makes people think of some particularly visible aspect of the system, rather than the total number of microstates available to the system as a whole. I think we can take that as read.
But Nonsuch wasn't asking about that. He was asking you specifically why you think there's any difference between on the one hand the thermodynamic entropy and on the other hand the information entropy (Shannon entropy) of the microstates given a macroscopic description of the system. Blathering on about the Bohr model of the atom is not an answer. Jheald 16:34, 7 July 2006 (UTC).

## A Quantitative question re information 'bits' and thermo entropy W numbers

I am not knowledgeable re the bit size of words, sentences or other forms of information and communication. From too long ago, I recall some 'baby calculations' of 6 letters to form a word but couldn't find details in my files. Yesterday, glancing at Pitzer ('Thermodynamics', 3rd edition 1995 [McGraw-Hill], I was reminded of an important question that I have wanted to ask of a person competent in such matters, as some of you are. Here's the background:

Pitzer was interested in the number of QM microstates as close to 0 K as experimentally feasible, i.e., the W, where S(lowest possible) = k ln W. Essentially, he assumed that the smallest change in S would be 0.001 J/K mol (his S/R equalling 0.0001). I took from his development a different thought: the least change in entropy that can practically be considered/calculated would be S = 0.001 J/K mol, even though one never sees practical values of entropy tabulated beyond 0.01 J/K mol. The math-trivial solution leads to a W = 10 ^ 3,000,000,000,000,000,000, a rather modest number for W, compared to standard state or reaction entropies for a mole of a substance.

My information-bits question: "Is this figure of ca. 10^10^18 in the range of bits in information content or information communication?" The usual entropy change in chemical reactions is, of course, in the 10^10^24 range. Again, "Are there numbers in info content/communication calculations that are in this range?"

My question is important in evaluating a phrase in this and other discussions of entropy increase as involving an increased "loss of information". Glancing at the example that I gave you -- a few feet ago! in this Talk Entropy discussion of ice and water, do you see how it is beyond human comprehension -- except by numbers of microstates, W -- to evaluate the 'amount of information that entropy reveals is for ice: 10 ^ 1,299,000,000,000,000,000,000,000 microstates. Now, do you instantly understand the 'information that is lost' for the water at the same temperature, or 10^1,991,000,000,000,000,000,0000,000 microstates? It isn't 'appearances' or 'disorder' or 'information' that is vital in evaluating thermod entropy change in science -- it's numbers.

Do you now see how inadequate (a nice word) are descriptions such as 'information' and 'lost information' if you want to discuss thermodynamic entropy change scientifically? Numbers, quantitation via numbers of accessible microstates -- coming readily via the approach to understanding entropy that I am bringing to you, and a major reason for its rapid and wide acceptance in chemistry -- is the only way to cope with 'information' in thermodynamic entropy change. FrankLambert 16:48, 3 July 2006 (UTC)

The sums as I make them:-
S = 0.001 J K-1 mole-1 gives σ = S/k = 0.001 / 1.8 x 10^23 = 56 x 10^18 nats mole-1 = 79 x 10^18 bits mole-1 = 10 x 10^18 bytes mole-1, or 10 exabytes per mole.
According to the exabyte article, the total amount of printed material in the world is estimated to be around five exabytes (presumably counting every copy of every book separately); the sum of human knowledge to 1999 (including audio, video and text) was 12 exabytes (presumably counting each title only once for all the copies); about 5 exabytes of storage space were created in 2002, mostly as hard disks.
It's good to be reminded that the quantitative amount of "missing information" represented by thermodynamic entropy is mind-boggling large. But I don't see that that represents any problem at all for "missing information" as a qualitative interpretation of thermodynamic entropy. -- Jheald 23:22, 3 July 2006 (UTC).
Secondly, I don't see what you're trying to say with the statement It isn't 'appearances' or 'disorder' or 'information' that is vital in evaluating thermod entropy change in science -- it's numbers. When used as a gloss for the word entropy, the "mixedupness" of the system (or equally the disorder) precisely is the numbers: no more, no less. When there are more microstates compatible with the macroscopic description, there is more uncertainty, the system is more mixed up, end of story. Jheald 00:15, 4 July 2006 (UTC).

Fantastic!! I greatly appreciate Jheald's kindness in supplying the information data re the total amount of human knowledge as of 2002 at around 18-20 exabytes. From that we may extrapolate very roughly to no more than 40 exabytes in 2006. Now, with an entropy (change) value of 0.001 J/K mol = 10 exabytes, a little more than a tablespoon of liquid water at 273 K (S = 63.34 J/K mol) is evaluated as containing 63,340 exabytes. That would 'mean' that the number of accessible microstates for the 18 grams of ice-cold water is equivalent to some 63,340/40 exabytes or more than 1,500 times all of the information in the world in 2006! That's pretty incomprehensible and yet that entropy value is small compared to, say, a gallon of gasoline.

Exactly! Isn't it great? Doesn't it just fill you with an irresistable urge to go out and channel Douglas Adams?
ΔS° is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the stacks at the Library of Congress, but that's just peanuts to ΔS°. Listen...
But just because it's rather further to Betelgeuse than going down the road to the chemist, it doesn't mean that they aren't both lengths, nor we can't measure them both in metres. Similarly, don't you think that it's a triumph for the human imagination, that we can recognise chemical entropy as information, and even quantify it — in bytes? Isn't that an awesome intellectual achievment? Doesn't it give you chills? Jheald 21:41, 4 July 2006 (UTC)
Preach it, Brother! Nonsuch 22:00, 4 July 2006 (UTC)

Because of his courtesy, I regret contradicting Jheald, but he is seriously in error regarding the basic problem of describing entropy -- for students in a class or inquirers of Wikipedia. Evidently, never having had to communicate with students in beginning chemistry classes, he is unaware of how difficult it is to transmit information accurately (and concepts, far more so) I keep repeating the need for that viewpoint because it is a fact that he, and some physicists in the group, do not seem to grasp: we who are instructors must describe and develop our subject matter in a way that both 'concrete-thinking' and more 'abstract-capable' are well served. The ultimate goal in physical science is that concepts can not only be linked to others to form a progression toward both a broader and deeper understanding, but, if possible, that each concept be loosely or precisely shown to be quantifiable.
'Appearance' or 'disorder' or 'mixed-upness' or 'information loss' are not valid adjectives or 'glosses' that lead to describing entropy quantitatively! They have been proven -- for over a century, in the case of 'disorder' and 'mixedupness' -- to insure a misunderstanding of the nature of energy change not only in students but instructors whose thinking has been misdirected by them. They do not lead to the idea that entropy is a readily quantified measure of an even more readily visualizable description of vigorously moving, violently colliding molecules that will inevitably occupy more space if they are not constrained. (And that superficial occupancy is describable/quantified in QM terms of energy levels and temporal accession to QM microstates.)
Jheald or anyone not teaching chemistry or physics certainly has the right to continue an individual opinion of the matter. But just as certainly, if Wikipedia "Entropy" is written to aid young students in science through mature adults who are not in science -- or those unfortunate ones in science who for generations were 'taught entropy' via the miserable traditional procedure in many thermodynamics classes of "do enough problems and you'll come to understand it" -- it should be written from a modern viewpoint of entropy instruction. FrankLambert 04:39, 4 July 2006 (UTC)

I remember when the direct equivalence of Gibbs entropy as being a form of Shannon entropy was first pointed out to me: it was a real scales falling from my eyes experience. Suddenly thermodynamic entropy was no longer some mysterious quantity with some strange, not entirely clear, voodoo connection with energy. Instead it was simply information, there in statistical mechanics because statistical mechanics is an inference process.
It was a real simplification, a real clearing of the decks moment.
Wikipedia should not throw obstacles in people's way by raising unnecessary barriers between Gibbs entropy and Shannon entropy that have no basis in physical content, and do not need to exist. Jheald 21:41, 4 July 2006 (UTC).

What a crock!! That "voodoo connection [of entropy] with energy" of Jheald enabled chemists and Ch.E.s for the last century to have fed the world (SAVED the third world from starvation for about 50) via trillions of tons of ammoniacal fertilizers, and benefiitted us with trillions of tons of high octane fuels, billions of tons of plastics, and thousands of tons of pharmaceuticals -- ALL due to use of thermodynamic entropy calculations "with voodo connection with energy"! The start toward understanding that connection is SIMPLE if you would only read what I carefully prepared for Kats and you in the inset paragraphs in the middle of the "Disorder is DEAD in introducing entropy to students/readers" above. The lower level, that which any 'concrete-thinking' individual can grasp, is what a major number of chemistry students in the US learned this past year! It was in their textbooks. I am glad that you agree that "Wikipedia should not throw obstacles in people's way" by introducing your own confusion to "Entropy ..in chemistry, physics and thermodynamics" that belongs in the Page to which you have not contributed any Talk, "Information Entropy"" FrankLambert 23:39, 5 July 2006 (UTC)

Let me try and clarify. Of course you take Σ pi ln pi, apply it to the disposition of energy and chemical species, and that's where the whole of thermodynamics, chemical equilibrium constants, etc., etc. all comes from. No disagreement from me about the off-the-scale importance of that.
But the point I was trying to get at is rather different: Is it relevant that you're going to be applying it to dispositions of energy, when you ask, where does the mathematical shape of the form Σ pi ln pi come from?
And the answer is No. There isn't anything specially relevant about the fact that you're going to be applying it to dispositions of energy that leads to the shape of that form.
Perhaps that's obvious in hindsight, and I should have known it from the start. But, like I said, I found that realisation a real step forward, a real simplification. Jheald 08:15, 6 July 2006 (UTC).

FrankLambert said "the least change in entropy that can practically be considered/calculated would be S = 0.001 J/K mol". This is patently wrong. Thermodynamic entropy is only macroscopically large when you consider macroscopic numbers of molecules. But the biochemists (and molecular biologists and biophysicists) who's understanding of thermodynamics you deride are obliged to consider the thermodynamics of single molecules. Experimentally accessible entropies are on the order of a few bits per molecule. Nonsuch 21:56, 4 July 2006 (UTC)

Reread my July 3 comment where I clearly give K.S.Pitzer (successor to Lewis and Randall's "Thermodynamics") as the source of the quotation. Of coursethat applies to a macro system! That's what one deals with in teaching the first couple of years about thermo entropy and with the vast majority of basic research in chemical thermo. The inapplicability of "entropy" to few molecules has long been a tenet of thermodynamics. Thus, I am fascinated by the possibility that you describe by "the thermodynamics of single molecules. Experimentally accessible entropies...". Could you please cite a lead reference? This is important. I must include it in my reading/thinking.
(Again) I was thinking of the Jarzynski identity, in particular the referenced 2002 Science paper. See also Fluctuation theorem. Nonsuch 00:09, 6 July 2006 (UTC)
{A side note, in no way did I deride the understanding of biochemists, molelcular biologists or biophysicists when I asked you and everyone to cite me ONE textbook in chemistry published after 2004 (and I know of just five out of 20 such new books) that still use 'disorder' in introducing entropy to students in 2006. When I wrote "excluding biochem because they have to be sloppy", I was actually quoting an author of a 7.0 pound biochem text who emailed me that there is not space nor time to reteach students who have been taught 'entropy-disorder', "we must write a bit sloppily to not upset incoming students who are not as well prepared as you propose..." It is the elementary' biochem text that is enormous and enormously burdensome to the beginning bio/biochem young person that I was criticising. BUT I see his point -- only for the next 2-5 years.)
O.K., conceded. You were deriding the textbook writers, not the practicing scientists. Nonsuch 00:09, 6 July 2006 (UTC)
Any researcher in biochem/phys MUST look closely at the viewpoint of entropy change as fundamentally a case of energy dispersal if s/he wants a thorough understanding of thermo and entropy change. Bits and bytes are cutesy but how -- in your research -- are they related to energy dispersal and thermodynamic entropy -- it's that basically that enables change and that's what counting the info will never tell you. Probable bits are the result of most probable energy distribution/dispersal.
(The biggest success along that line, emailed me in feedback from my sites, was an Australian grad student in thermoplastic rheology of thermosetpolymers. Bogged down in the third of fourth year of research, lots of data, struggling for conceptual unification for thesis, the student read my stuff, turned the research advisor's view away from (stupid) 'entropic force' to thinking about 'energy dispersion' and was able to complete the dissertation smoothly with total agreement by the prof and got a grant for post doc work, (and put a quote from me on the diss. frontispiece, that I had forgotten "Energy spreading out is the function of which entropy is the passive measure." ) Try focusing on that when you up against it in figuring out why the bit and bytes come out the way they do. (But send me a copy of the dissertation :-) FrankLambert 23:39, 5 July 2006 (UTC)
Funny that. Just a few weeks ago I overheard a professor complaining about a graduate student who didn't understand, or perhaps had never heard of entropic force. Must be a different student, since I think they were working on biological polymers. My point, of course, is that many experts don't agree that "entropic force" is stupid. Nonsuch 00:09, 6 July 2006 (UTC)
No sweat. A lotta people believed in phlogiston too. Wait til your 'many experts' find out how stupid is their view. However as the history of 'disorder' in entropy shows, they have to hang on to their views, wrong or not. Since you're young, they'll die before you and you can remember back to this great day when you found out that entropy, a measure of something (guess what!), couldn't conceivably, conceptually be a force for anything. Molecular motional energy is always ready to DO something , to enable a process that entropy then measures. Read the last part of my response to you in "Out of Hand." FrankLambert 22:20, 6 July 2006 (UTC)
May I ask the couple people involved with this disucssion to give a (very) short recap of exactly what the issue under argument is? I don't know much about how the concept of information is applied to entropy, however I know from experience and study that fluffed words like "disorder" lead basically to lies and confusion that are meant to be somehow simpler to laymen. Fresheneesz 04:32, 7 July 2006 (UTC)

## Out of Hand

"equating Entropy with disorder is not only unwise, it is a concept that fails actual experiment." Can you back that provocative statement with an actual citation? The peer-reviewed source you refer to is Frank, so that doesn't exactly add extra weight to your side. You're ignoring the vast peer-reviewed literature that knows that entropy isn't "dispersal of energy". For starters, entropic force, residual entropy and Landauer's principle.Nonsuch 14:08, 6 July 2006 (UTC)

Nonsuch, I was trying to appear 'lite' by tweaking you about your care/diligence in reading (and understanding) the non-value of 'disorder' in thermodynamic entropy in "Appeal to Authority" above. Now, quite seriously, from your non-acknowledgement of my response: YOU DON'T READ CAREFULLY!
{Others, check his "Appeal to Authority" where he tried to support the validity of using 'disorder' in entropy by quoting three physicists. Unfortunately, two of the three (one was Feynman) actually said "entropy is a measure of/measured by the number of microstates" exactly what I have been trying to persuade users in this site to replace for 'disorder' -- a quantitatively/conceptually useless word in THERMODYNAMICS (a topic that is today and forever 'heat'...'energy').
Now unfortunately, Nonsuch again exposes his lack of diligence by not reading citations that have already been presented to this list: Check Jheald's ref to Styer (at the end of "Removed Confusing Text") D.F. Styer, Am. J. Phys. 68 1090 (2000). Have you not read the ref. to Leff (online at http://www.csupomona.edu/~hsleff/EntropySpreadingSharing.pdf ) Here is a prof of international renown for Maxwell demon books who talks about the confusion of physics majors who have to cope with 'disorder' as related to entropy. AND states that "spreading and sharing [molec. collision] energy" clarifies the entropy approach. That's dispersal of energy, to me!
Actually it was Nonsuch who wrote warmly about the Styer article. I just added the web-link. Jheald 10:53, 7 July 2006 (UTC).
And 'residual entropy', that example of the triumph of configurational/positional entropy and of the 'necessity' for classic stat mechanical calculation/explanation of entropy in solids [what happened to Jheald when I challenged him on his understanding of energy distribution in alloys?!]. I told Nonsuch and others (just prior to the start of "The Full Monty" , that an article is in press dealing with CO 'residual entropy' as simply due to two different energy levels being frozen in at the fusion temp equilib, but unchanged to 0 K. I also urged you to check Hanson, J.Chem.Educ, 83, 2006, p. 581 that would chill your heart by being the first article to show the equivalence of energy-based entropy to stat mech position-based (configurational) entropy. There are some articles that you really must become familiar with before challenging Astrobayes or anyone about there being any value to 'disorder' in thermodynamics. THERMODYNAMICS, that is, in unabashed capitals.
Sorry, Frank, for not getting back to you. I have to admit, I didn't follow what you said one should think about the 0 K limit. Could you go through it for me again? Suppose we have a crystal, with trace impurity of some other substance. The impurity changes the melting point, a change we can in part attribute to the entropy of the different possible configurations for the impurity molecules (or if you prefer: the different possible molecular motions of the impurity molecules, if we count different positional configurations as different motions). But now we chill the whole thing down as near as we can get to 0 K. The entropy is still there; it's now "frozen" disorder. But does it still make sense to talk about it as different possible molecular motions, now that there isn't any motion? It's the states that count, not the motion. Or so it seems to me. Jheald 10:53, 7 July 2006 (UTC).
Now to the funniest. Going back to your first sentence, Nonsuch, there ain't no peer-reviewed literature that KNOWS (states, claims) that entropy isn't "dispersal of energy"!! Unfortunately, embarrassingly present in Wikipedia, your great example of "Entropic Force" was started by a youngster in physics. Now look at the definition: "entropic force acting in a system is a macroscopic force whose properties are primarily determined ...by the whole system's statistical tendency to increase its entropy." How beautiful! Systems have inherent 'statistical tendencies to increase their entropy" -- the ultimate in von Neumann's joke..:-( .Who needs an energetic component for water in a beaker to boil...there is an inherent stat tendency for it to increase its entropy by raising its temperature. Hot dog. I want to buy stock NOW in any 'entropic force' company.
I think you're misunderstanding that line. The entropy of physical systems has a tendency to increase. That tendency is statistical, becase for mesoscopic systems, entropy can (sometimes) go down as well as (usually) go up. Jheald 10:53, 7 July 2006 (UTC).
The point is, this is information "entropy" gone wild. There is no such entity/force/concept as 'entropic force' -- what ENABLES "a statistical tendency to increase" is ENERGY, in particular in chemistry, is the MOTIONAL ENERGY OF MOLECULES. Can't you info "entropy" guys see that entropy is a two-factor function, as I have said again and again?? I see perfectly that Shannon information/etc. is indeed a fine math description of what happens to a bundle of molecular energy AFTER/DURING a proces IN WHICH THAT MOLECULAR ENERGY IS ALLOWED TO DISPERSE -- when a gas expands or fluids mix or a system is warmed by surroundings. (But that math description, that yields numbers of ways, is terribly sterile conceptually without quantal views of energy levels and microstates.) Check http://www.entropysite.com/calpoly_talk.html
Technically of course, it's not the energy that causes the entropy to increase. It's the loss of useful information, reflecting the way you're modelling the system (eg classical coarse-graining; or the discarding of information about correlated quantum subsystems). Jheald 10:53, 7 July 2006 (UTC).
Now, aside from the foregoing, but in a final part of an answer to Nonsuch , there have been 3-4-6 articles along this line [2] in the last decade, of small particles in a fluid being caused to form an orderly array --BUT the cause is actually what one would expect : a greater dispersal of energy in the solution (the researchers usually mis-see it as a greater possible increase of entropy in the solution than decrease in the particles!! Oh that wonderful 'entropic force' that the Australian grad student knocked out of the prelim of the thesis I told you about. Energy dispersal wins again. FrankLambert 21:59, 6 July 2006 (UTC)

Frank has made quite an impassioned appeal above (see eg under Authority, Shmathority) that the article should be made much more chatty, much more introductory, and much more focussed on getting over the idea of entropy to beginners, through a much more extensive exploration of the idea of energy naturally dispersing.

It may well be the case that such an article would be a useful addition to Wikipedia. But can I suggest that if someone does want to create it, they create it as a new breakout article from the current page. Don't scrap the current page to do it.

Because I think SadiCarnot did a very useful thing back in April, when he took what was then a very long, involved and discursive article, split most of it out onto separate pages, and put the article into essentially its current shape.

What the article represents now is a quite terse, quite tight, "helicopter view" pull-together in a nutshell; giving a quite short map of some of the different ways (all valid, all related) in which entropy can be analysed, pictured, discussed and understood.

These include, for example

• a measure of equalisation; in particular of heat becoming more evenly distributed
• a measure of energy unavailable to do useful work
• dQrev / dT
• the number of microscopic states compatible with the macroscopic description
• an amount of "missing information"
• the variable in the 2nd law of thermodynamics
• entropy described as "disorder" or "mixedupness"; with a caveat that that doesn't mean the disorder just of the most obvious bits of the system.
• plus a mention of entropy in black holes and entropy in cosmology.

Now I'm sure that there are all sorts of improvements that could be made. But at the moment, if that is the article's aim, I think it actually delivers it quite well. IMO, the many different mutually supporting ways that entropy can be thought about are presented so that they actually do cohere quite well; and the interested reader can rapidly navigate to more specific articles which explore particular facets in more detail.

I'm sure the article will continue to evolve and improve. But for myself, I wouldn't like to see the range of it being reduced; nor would I like to see the wordcount getting much longer. IMO, it has a particular purpose, and the shape and structure as it is at the moment helps to achieve it quite well.

I don't have a problem with somebody wanting to write a more gentle, discursive introduction for beginning chemistry students, either as a "breakout" article from the central page, or as an external link. But I do have a problem with articles that claim theirs is the only way to think about entropy. I think that is a problem with some of Frank's articles; and I think that some of the conflict that poor Astrobayes is in stands as quite a warning of what it can lead to.

The truth is that it is useful to be able to think about entropy in different ways; to know how (and why) they are equivalent; and to be able to move seamlessly between them. That's my 2 cents, anyway. Jheald 09:58, 7 July 2006 (UTC).

I agree with Jheald that currently the article provides the appropriate definition and explanation of the various aspects of entropy, and it should not be revised according to Frank's suggestion involving the concept of "energy dispersal", which is really vague, as I wrote above (and reminds me of Feynman's wakalixes: search for "Judging Books" here). The fact that "concrete-minded students" (in Frank's words) can buy this concept more easily than the correct ideas should not be a reason to encourage its use. I disagree with Jheald that such a discussion should be included elsewhere in Wikipedia. In my opinion, it has very little value, so it should not be included at all. Yevgeny Kats 18:42, 7 July 2006 (UTC)

Kats' comments are insulting to me and even more to those many textbook authors who have adopted my approach to entropy. I urge that Kats' immature and unsupportable statements be ignored.
"Specifically because he postulated on his own, not from my writing that energy dispersal in thermodynamics would have to have a separate definition "for every type of physical process", I wrote a page for his benefit (indented in "Disorder is DEAD ..." above). In it is shown in detail the power and universal applicability of the concept -- some indication of why it has been so widely accepted in print (not merely in chat groups around the cyclotron cooler).
Kats only glanced at my first paragraph, evidently. Thus, because he has only had experience with beginners as a TA in teaching superior physics students at Harvard, of course it is easy for him to dismiss the enormous group of 'concrete thinking' students across the US. When these beginners are desperate to get some grasp of entropy that their less brilliant TA or professor does not provide, they'll very probably hit the Internet and Wikipedia for help! But honors students can also be greatly aided, if the TA is not competent, by seeing in W Entropy a brief introduction to the energetics of entropy, to quantized energy levels, and their relation to an increased number of microstates, the measure of an increase in thermodynamic entropy :-) FrankLambert 21:50, 7 July 2006 (UTC)

Fresheneesz, I don't think that given examples of how brilliant scientists described entropy in their brilliant prose in support of using similar phrasing here counts as original research. There are two related points at issue, one of terminology (Roughly, is "disorder" a useful word to use when trying to explain what entropy is) and a deeper, but related dispute over what exactly is entropy anyways.

Frank, thank you for your reply to the card shuffling example. I think I may more or less understand your POV. To summarize, you think that (thermodynamic) entropy is the dispersal of energy, whereas I think entropy is a 'measure' of the dispersal of energy, or more generally a measure of information (or roughly mix-up-ness, disorder, or randomness), there being examples in thermodynamics of entropy being carried by non-energetic degrees of freedom. These different viewpoints lead to the disagreement over describing entropy as "disorder" since that description, omitting any reference to energy, isn't compatible with thinking about entropy as "dispersal of energy"? [User; Nonsuch...]

think that we're far closer than you conclude. Both at the end of my "Disorder" segment above and in "Information "Entropy"" (and those quotation marks are a necessity for distinguishing, rather than disparaging), I pressed my essential new idea of entropy as a two-factored change. To repeat here:
"An increase in thermodynamic entropy is enabled in chemistry by the motional energy of molecules (that, in chemical reactions, can arise from bond energy change). However, entropy increase is only actualized if the process makes available a larger number of arrangements for the system’s motional energy, a greater probability of an increased distribution for the system’s energy."
"The two factors, energy and probability, are both necessary for thermodynamic entropy change but neither is sufficient alone."
"In sharp contrast, information ‘entropy’ depends only on one factor, the probability factor, -k Σ[Pi log Pi], where k is an arbitrary constant that never is required to involve energy, as does kB." (Further, merely substituting kB for k does not magically alter a probability of shuffled cards or tossed coins so that it becomes a thermodynamic entropy change! A system must inherently, integrally possess energy transfer entities such as moving molecules (or, as occasionally in physics, photons and phonons).
So you see why I can't accept 'disorder' in thermodynamic entropy as anything but a continuance of the old hand-waving of your and my profs and all their predecessors in chemistry and thermodynamics? The 'package' in your information work may certainly be named what you want to call it: 'disorder', whatever. However, in thermo entropy, energy is always implicit and part of the process, it and the final microstates are many but they are discrete, individual -- enormity of a number of microstates does not mean an immeasurable glob or smear or mess that 'disorder' implies. (All of this seems so silly to me. It all can be omitted simply by your discarding a misleading, confusing, ill-defined non-scientific word from a scientific -- or a mathematic -- field!)FrankLambert 21:50, 7 July 2006 (UTC)

You correctly identified the limitation of the card unshuffling example, namely aren't all orderings of the cards equivalent? So let me modify the example in order to removed that deficiency. Instead of one pack, I hand you 2 randomly shuffled packs and ask you to put the second pack in the same order as the first pack. This procedure clearly reduces the information entropy of the cards. [User: Nonsuch...]

[Forgive me for breaking up your paragraph; maybe ill-mannerly in Wiketiquette but essential, I feel, for optimal communication] Maybe this is the KEY to all your texts and co-workers to continuing to identify information change with thermodynamic entropy change!!! You give me "a system of the two packs" and want me to do something to it -- with me ACTING AS THE SURROUNDINGS. Seemingly a PERFECTLY GOOD THERMO "system -- surroundings" interaction in which a THERMO change in one demands a THERMO change in the other, right?
BUT LOOK -- the cards in any orientation, any state of handling, organization, shuffling are UNCHANGED in each card's and any arrangements' thermodynamic energy content and entropy content. They are immobile, non-interacting 'particles'. Cellulose at the same temp before and after, in this pattern or that pattern. Thus, there is NO thermodynamic entropy change in the "system"....so what you go on to write in the next paragraph is not correct. Nothing has thermodynamically happened in the system so there's no need for any change in any other part of the universe. (And it isn't a matter of scale!! My first argument in the shuffled cards area was with a non-Occidental College phys chem prof, and he said, "But if you have a mole of cards..." and I said "Would they have any more energy interchange than..." and you should have seen the quick change in the look on his face...!! He was my first 'convert'. He knew instantly what he'd been talking about for years was wrong :-)FrankLambert 21:50, 7 July 2006 (UTC)

To compensate I have to increase the entropy of some other part of the universe, perhaps adding energy to a heat bath to increase the thermodynamic entropy. The only fundamental difference between molecules and cards in this example is one of scale. The thermodynamic change due to unshuffling is tiny compared to any macroscopic scale. Nonsuch 16:41, 7 July 2006 (UTC)

## Apology

First, I owe an apology to Nonsuch and to Jheald for speaking harshly to them when I felt that they had not taken the trouble to consider what they or I said. That's not my prerogative nor an objective judgment of their diligence. (I greatly appreciate their courtesy in not responding in kind.) I get overly excited by any discussion involving entropy. The correct presentation of a basic understanding of thermodynamic entropy to undergraduates in chemistry has been my primary focus for about 8 years. My good luck in discerning what is now accepted by most chemistry text authors has been as amazing to me as it is unknown to those not in chemistry instruction.

Second, I have written too lengthy pieces in this Talk page. That was certainly not from a desire to write [I have papers to do before I pass on!!], but to explain clearly a modern view of thermodynamic entropy in chemistry as measuring the spreading out of energy from being more localized to becoming more dispersed, spatially and temporally. [The latter 'temporally', ties the idea to Leff's interpretation of a system's constantly changing per instant from one accessible microstate to another as an 'entropy dance' over time.] One of 'the modern view's' many advantages, I believe, is that even concrete-thinking students can readily 'get' the idea of active molecules spreading out in space -- both in 'thermal' or 'configurational' entropy, while that 'half of the whole picture' seamlessly fits into the next level of understanding: quantization of energy levels, microstates, etc.

The profound newest view -- that entropy is a two-factor function (please click on the CalPoly seminar [3]) -- explicitly clarifies the difference between thermodynamic entropy and information 'entropy' in my opinion. (It is has passed the first barrier of article peer-review with only one dissenter now being countered.)

With Jheald, I agree that it is time for a focus on the actual Entropy page. Because I believe that naive readers will be the most frequent visitors, but NOT the only visitors of course, the initial introduction should be for them -- but NOT in any chatty style. (Sorry; the suggestion made in the Talk above was fast-typed chatty, but no way should it be such in the Entropy page.) I'll work on a 'possible' late today, of course subject to review.FrankLambert 18:12, 7 July 2006 (UTC)