Talk:Second law of thermodynamics/Archive 3

Separate talk page for Second Law and creationism / organised systems

Moving the whole discussion about the Second Law, creationism, and the evolution/stability of organised systems to Talk:Second law of thermodynamics/creationism Jheald 13:29, 5 November 2005 (UTC)

False/Misleading Explanation?

I believe the following explanation is false or at least very misleading, so I intend to correct it after a quick review in my stat-mech book. I post my intentions here so that if someone things I am wrong (and the current article is correct), we can have that discussion first.

"Since the universe is tending towards a greater entropy (expanding over time, with lower energy density), all work processes within the universe also tend towards a greater entropy. "

I believe the above is false or very misleading. The 2nd law of thermodynamics is not caused by the expansion of the universe. The 2nd law is believed to apply to any closed system, and so it is not caused by the expansion of the universe. The 2nd law is believed to be a macroscopic statistical property that can be derived from the microscopic laws of physics (although I don't know whether or not anybody has managed to do this yet in a rigorous way.)

Does anybody disagree with me, and believe the 2nd law is held to be due to expansion of the universe? If so, is there an academic paper or text book you can cite? Thanks. Bmord

I'm wondering if you didn't just misunderstand the quote. Certainly your interpretation of it was different from mine. I honestly wasn't given the impression from the quote that the second law was actually caused by the expansion of the universe; though it certainly is true that the entropy is increasing as our universe expands.

--Wade A. Tisthammer (10/2/2005)

A does not cause B, and B does not cause A - this is why I figured I would remove it. The basket ball does not fall down due to increasing entropy, and it does not bounce back up because of increasing entropy. If the universe were to stop expanding and start falling back in on itself for the 'big crunch' due to gravity finally overwhelming leftover momentum from the big bang (as has at times been predicted), this again would not be due to increasing entropy. (The fact that the basketball doesn't bounce quite as high on each subsequent bounce - now that does have something to do with increasing entropy.) (I should mention that I have made the edit - apologies for not using the edit summary feature on the main article.) Bmord

I thought we had settled this, I'm not sure why it reappeared. Discussion of this has now moved to a lower section ('Deletion of part related to universe collapse'), refering to a more recent reincarnation of this popular mistake. Bmord 18:39, 5 November 2005 (UTC)

Statement of Law

Could this article please begin with a concise statement of the 2nd law?

---

Free Lunch

Should it be mentioned that this is often reduced to "There 'aint no such thing as a free lunch"?

---

microstates and macrostates

the only way i have ever understood this stuff is someone explaining macrostates and microstates. they reduce it to a small game of black and white chits on a board or something. or maybe it was coins, and heads and tails. i cant remember where i saw this, but it sure would help people reading wikipedia if someone could do the same here.

Link between heat cycle and entropy ?

I'm trying to explain the 2nd law in simple terms. This is still very much a work in progress. Any help welcome. I have some difficulty making the link between the fact that no heat cycle has a 100 % efficiency, and the fact that disorder is growing: why are those facts equivalent ?? I'll have to do some more research to find out... Pcarbonn 20:41, 22 May 2004 (UTC)

Makes it seem like perpetual motion machines are possible

Quote from page: "Any device that violates the second law of thermodynamics would be called a perpetual motion machine of the second kind. One example of this would be a device that can do work such as pumping water, simply by taking energy from the air." Though I'm not sure what the definition of a perpetual motion machine of the second kind is, it seems to me that this paragraph is unclear since readers will think "But that's possible - people have been using windmills for ages - so perpetual motion is possible?" Perhaps change this to "by taking heat energy from the air. ( Or better yet, the perfect example would be a light powered the solar panel that it was shining on" --Jomel 15:23, 13 Aug 2004 (UTC)

Hawking

In 1988, Stephen Hawking, in his book A Brief History of Time, used the following line of thought to show the effect of the measurement mechanism : if, contrary to the second law, the entropy of all systems decreased with time, our brain would also go from ordered to disordered over time, and we would not be able to remember the observations we made (because in that case our brain would go from disordered to ordered, which would be a contradiction; see arrow of time). In other words, we would not be able to observe a world where the inverse of the second law would hold everywhere.

I dont remember Brief History well enough, but stated this way it is patent nonsense.

• actual law: entropy of all closed system increases
• logical negation: entropy of some closed system decreases
• "inverted arrow": entropy of all closed systems decreases
• nonsense: entropy of all systems increases/decreases

Entropy of open system can decrease. Example: booting computer, bits in RAM go from disordered to ordered, entropy decreases. (But: it the process electricity is converted to heat and in closed system "power plant+coal+atmospehere+my computer" enropy increases.) Our brain is like computer.

if the entropy of all systems decreased with time, our brain would also go from ordered to disordered over time

Bad implication - entropy decreases, system go from disordered to ordered.

"closed systems" in link

The answersingenesis link says "A closed system exchanges energy but not matter with its surroundings." This is incorrect, right? A closed system is defined as exchanging neither? - Omegatron 18:16, Jan 3, 2005 (UTC)

It isn't relevant whether the claims at links are correct or not.

I believe it is an issue of changing nomenclature. For some, an Isolated system refers to one that exchanges neither energy nor work. In this case, the entropic definition of the Second Law of Thermodynamics is described as only applying to Isolated systems. Sometimes, a closed system in Thermodynamics is described as cut off to energy, and then the Second Law of Thermodynamics is restricted to closed systems. That is standard creationist pseudoscience mixing the two halves together to support their biblical literalism.

bad example

"One example of this would be a device that can do work such as pumping water, simply by taking energy from the air."

I don't understand what this example is trying to show. A hidden source of energy would be something like the potential energy of a water tank being physically above an outlet. Maybe try to think of a real perpetual motion machine claim and how it worked. - Omegatron 17:32, Jan 3, 2005 (UTC)

2nd law question

I've got a question about the 2nd Law. It states heat does not spontaneously flow from cold to hot bodies . What about, say, magnifying solar power here on Earth with lenses/mirrors/whatever -- would the maximum temperature that one could achieve on Earth merely by focusing solar power be at most the surface temperature of the Sun (5800K, which is what the blackbody radiation curve of the Sun corresponds to)? I've heard, unreliably, on a few sites that this is the case, though no one indicates why.

(For example, this site claims that a large solar magnifier should attain "the surface temperature of the Sun).

This all makes sense from the POV of the 2nd law, but it seems like if you could concentrate, say, 100m^2 of solar energy (at 1kW/m^2) into a tiny area, you'd have an enormous amount of energy in a small area, and I don't understand why it would be limited by the temp. of the Sun. Also, it's obvious that you could convert the same light into electricity, and use that electricity to make temperatures as high as you want.

Could anyone shed some light onto this puzzle? Schmiddy 19:23, May 11, 2005 (UTC)

The resolution lies in the definition of heat. Heat is the diffusive flow of thermal energy, which is stored in the undirected motion of atoms and molecules. In contrast, work can be thought of as the directed flow of energy. In the example you give, the stream of photons coming from the sun would be classified as work, not heat (in the language of thermodynamics). There is nothing stopping you from focusing this flow of energy into a fluence far higher than the Sun produced. You can enable energy to flow from a colder body (the Sun) to a hotter body (your hypothetical target on Earth). However, until those photons jiggle the atoms and molecules in your target to increase its thermal energy, the substance that was flowing was not heat, but work. JMM 18.115.5.159 14:35, 26 September 2005 (UTC)

No, I don't believe this is the resolution. When we start applying terms like "substance" to describe work, we should get suspicious of our thinking. This puzzle is actually very insightful and subtle, I thank the author for asking this question. If we can make heat transfer in the form of blackbody radiation flow against a heat gradiant, then why couldn't we build a perpetual motion machine? For example, imagine a closed system composed of two blocks A and B of matter separated by vacum, with whatever lens arrangement you wish so as to make blackbody radiation from block A warm block B to some temperature that is higher than A. Then, connect these with a heat engine, and you have a perpetual motion machine of the 2nd kind! The answer must be that this lens arrangment is impossible, because as the temperature of block B (in this case, some spot of earth's surface) approaches the temperature of block A (in this case, the Sun), then B will start to glow - the rate at which B cools itself through blackbody radiation (probably dumped back onto A) will come to match the rate at which A is transfering heat to B. So now, anybody want to take a stab at explaining why either you can't use solar pannels and electricity to violate the 2nd law, or why such an arrangment wouldn't actually be a 2nd law violation?

Yes, that is indeed the resolution. Or at least, your arguments to the contrary are not convincing. Let me address them one by one. First, your problem with the "substance"/"work" terminology: if you are going to discuss a thermodynamic issue, you should be familiar with thermodynamic terminology. It is quite normal to discuss the work done on an open system by the addition of a substance. In this case, the open system is the target on Earth, and the addition of photons from the Sun constitutes work. Thermodynamically, it is not heat because it is not yet in the form of diffusive thermal energy of atoms and molecules. This is discussed in Atkins' Thermodynamics: Elements of Physical Chemistry, which I happen to have on hand, and many other books, I'm sure. Note: in the field of heat transfer and essentially everywhere except thermodynamics, photons are considered to be a form of heat. Yes, this is inconvenient.

Second: if I understand your argument correctly, you say that heat transfer in the form of blackbody radiation against a heat gradient is impossible. You claim that this effect would allow us to use the photons from block A to warm block B to a temperature $T_{B}>T_{A}$, and then in turn warm block A to an even higher temperature $T_{A}>T_{B}$, etc. But I didn't claim this, nor did Schmiddy. It is pretty easy to see that the energy of block A is reduced when it emits photons, and no real optical system could transfer 100% of this energy to block B. Even fewer photons could be transferred back to block A. The law of conservation of energy is not being broken. Running the process in reverse never transfers enough energy back to the Sun to replace what it had in the first place. So your conclusion that the arrangement is impossible because it would create a perpetual motion machine is faulty. So how can we possibly heat block B to a temperature higher than block A? The key is that the system is not symmetric; block A is far larger than block B. We are talking about transferring some of the energy coming from a very large object (the Sun) to a very small object (the target). That amount of energy happens to be enough to heat the target to a temperature greater than the temperature of the Sun. Remember, while energy is a conserved quantity, temperature is not. You can heat something to an arbitrarily high temperature if it's small enough, as Schmiddy presumed.

Third: I want to address your comment about the radiation flux from B to A limiting the temperature of B to $T_{B}=T_{A}$. I've given a lot of thought to the original question, and for a long time I thought that this must be the answer. But I'll bet that you haven't actually done this calculation, because it turns out not to be the case. The rapidly increasing (fourth-power) radiation from block B does not prevent us from increasing its temperature above the temperature of block A. Here is the calculation: consider the Sun, with temperature $T_{A}$, and a plate some distance away in a vacuum with area $A_{B}$ and temperature $T_{B}$. (It's going to be hard to keep the plate solid when its temperature is higher than the Sun's, but let's assume it's got a very high melting temperature.) Also assume the plate's emissivity is 1, though you don't have to (it just makes the calculation simpler). Finally, say that one face of the plate faces the Sun, the other face faces outer space. With mirrors I'm going to reflect all of the photons leaving an area $A_{A}$ on the Sun towards the plate. The radiative power incident on the plate from the Sun side is $\sigma A_{A}T_{A}^{4}$ and from the outer space side is $\sigma A_{B}T_{inf}^{4}$. Note here that $\sigma$ is the Stefan-Boltzmann constant and $T_{inf}$ is the background temperature of outer space, 3 K. Simultaneously, the plate dissipates radiative power $2\sigma A_{B}T_{B}^{4}$. What do you think the ratio between $A_{A}$ and $A_{B}$ has to be to get the plate twice as hot as the Sun, or $T_{B}=2T_{A}$? Work it out. It's actually only 32 for $T_{A}>>T_{inf}$, which is certainly the case here. So radiative dissipation would not limit us from getting temperature of the plate higher than the temperature of the Sun. The solar power folks who run mirror farms actually do a similar calculation to make sure they pump enough oil/water through their system to prevent the structure from melting.

So your arguments appear to be flawed, and I therefore stand by my claim that the Second Law of Thermodynamics does not prevent energy transfer against a temperature gradient, as long as the energy transfer is in the form of radiation, not diffusive heat. The Second Law also doesn't prevent you from collecting solar energy, storing it in a battery, take the battery to a lab, and using the energy to heat a chunk of something to a temperature higher than the sun. It only applies to diffusing thermal energy.

I hope this is clear. If there's an error in my discussion above, please point it out. Thanks, and sorry for not signing in before. --Glengarry 23:29, 4 October 2005 (UTC)

No problem regarding not loging in - in fact you just shamed me into creating an account. :) Sorry if I dismissed valid jargon too, my tone was inappropriate in any case.

I did not say your thought experiment suggests a perpetual motion machine of the 1st kind - the kind that violates conservation of energy. I agree that it does not. I did not say that it permits some ever-increasing cycle of heat where total heat increases indefinitely, sorry if I was unclear. I said it suggests a perpetual motion machine of the 2nd kind, not the 1st kind. Yes, you are right, your thought experiment conserves energy - my objection is that it permits perpetual recycling of waste heat energy. Let me be more specific about the perpetual motion machine:

Enclose the sun in a giant sphere that is perfectly mirrored on the inside, so that no energy is lost to space. (If you object this is impossible, then do whatever you like to give ourselves a closed system of finite size.) Now, put a small hole in this to accomodate your favorite optic system, which focuses an image of the Sun onto a tiny clump of matter, such that this tiny clump is hotter than the Sun. Enclose this tiny clump in perfect mirrors so we don't leak energy. Now, connect this hot clump to the cooler sun with a sterling cycle engine, use it to power useful machinery. (Put this useful machinery inside this giant thermos bottle that we constructed so we don't lose energy there.) This engine will run forever. Nevermind that you will run out of hydrogen, blackbody radiation alone will keep this going forever. Clearly, this must not be permitted. It does not create energy, but it does recycle waste heat energy indefinitely. I'll make you a deal - if you try to show this inifinite motion machine (of the 2nd kind) that I describe does not follow from your reasoning, then I'll try to find the hole in your calculation. This way we take on each other's points head on. :)

Btw, I think I figured out why you can'd do this indefinitely with solar panels either in a closed system - and the explanation highlights the fact that solar panel effeciency must always fall as its temperature rises. This is certainly true of today's solar cells, but apparently the laws of physics tell us it will always be true. I'll wait until we agree about optics though, first. But here's a teaser: the reason you can't do this trick with solar cells forever is the same reason why you can't power a solar cell off of its own blackbody radiation. -- User:Bmord 2:28, 5 October 2005 (UTC)

Aha! I found the problem in your calculations - and it wasn't in the math. It is in this statement right here: "With mirrors I'm going to reflect all of the photons leaving an area of the Sun towards the plate." This is physically impossible. As you imagine different contraptions with mirrors and lenses, you'll keep bumping into a annoying tradeoff: you can have precise control over angle, or over position, of the photons - but not both. Here on earth, the form this takes is you'll find a limit to how small you can focus the light from the Sun. You can not focus it to an infinitely small point - at best, you can reduce the light to a perfect image - you will basically have constructed a camera. Now as you get very close to the Sun you can attempt different things like fiberoptic funnels - but some of the light will always end up going the wrong way, and the greater the ratio of source surface to target surface, the less efficient your system will be. What you are battling is entropy in the light itself. (Random tangent - you might enjoy reading about light-based refrigeration. You can make things cold by shining laser laser light on them if you do it just right. This can happen b/c the heat entropy gets dumped into the light itself. I'll see if I can find a link, but basically you play tricks with spectral lines and laser frequency such that only those molecules traveling towards the light can absorb a photon, which they view as higher-energy since they are traveling towards the photon. they then re-emit it at some point later, on average at a higher energy, with the difference coming from the difference in kinetic energy between when they absorbed versus when they emitted. So, you see, light can and does carry heat entropy. You use a laser because the laser produces very 'cold' (orderly) light.) -- User:Bmord 3:00, 5 October 2005 (UTC)

Ok, I'll assume we agree now on optics. The solar panel version though is more interesting. I think the answer must be that solar cells must stop working as they get hot - for surely you can't power it off its own blackbody radiation. So, the solar cell must be cooler than the sun that shines on it, if it is to produce electricity to power a heater. But no solar cell is 100% efficient - some light that strikes it will be converted to heat, which in a closed system must eventually warm the cell. I bet the point where it stops warming, in other words the point where the light converted to heat energy is exactly balanced by heat loss due to blackbody radiation, must be at the point where it can no longer produce electricity. So yes, solar panels in the short term can be used to produce heat greater than the sun, but only temporarilly. This is only possible in the short term, and only because you started out with a useful heat gradient. Bmord 07:39, 28 October 2005 (UTC)

Huh, this points to some very general observations. For example, the biosphere couldn't work if the Earth were uniformly illuminated from all directions. The biosphere can derive useful energy from the sun only because it is warmed on one side and cooled on the other, or warmed during one part of the day and cooled during another. The biosphere can derive useful energy from the Sun only because it can tap into the flow of solar radiation as it flows from a hot place to a cooler place. Good thing the universe isn't of uniform warmth... The form this must take is that photosynthesis must also become impossible as a leaf's temperature approaches the temperature that produced the blackbody radiation that it is capturing. Bmord 18:35, 5 November 2005 (UTC)

causality

This article mentions the Second Law can be reduced to the Law of Causality. However, the linked article on causality never offers a scientifically viable definition of the law, even in the "physics" section of the article. I feel like this is extremely unsatisfying. The whole subsequent paragraph is based on the "Axiom of Causality". An axiom has to be extremely explicitly stated and it isn't here, nor anywhere else on Wikipedia as far as I can tell.

Clarify why the 2nd law is true

I'm not sure I get it entirely, so probably others wouldn't: If using the transfer of heat from a body to a colder one until both are the same temperature is the one and only way we know to convert heat into another kind of energy, it should be written in the article. Then, I guess heat can't be entirely converted because only half of the difference in heat is transfered (so even with the recipient being at absolute zero temperature it wouldn't get all of it) and only the heat that is transferred can be transformed (probably only a fraction of that, here again the article didn't inform me).

If it is so, it should be mentionned. It should also be mentionned either that it has been proved that there is no other way or that there may be a way that we don't know about.

If there is another way, then I don't get what prevents heat from converting back into other forms of energy. At all.

Thanks for the explanations, for me and for all wikipedia readers in advance.Jules LT 18:21, 1 September 2005 (UTC)

Wow, it's nice you all jumping in to help like that, don't answer all at the same time... Jules LT 13:34, 8 September 2005 (UTC)

OK, maybe I just wasn't clear enough: WHY THE LAW IS TRUE IS ENTIRELY UNCLEAR IN THIS ARTICLE.

• Do we know an explanation as to why it is true? Or is it just that it's never been proved wrong?
• Is the flow of heat from a body to a colder one the only thing that can be exploited to create another kind of energy?
• Does the idea that all the heat can't be converted into other energies stem from the fact that only half of the difference in temperature (for equal mass bodies) or so will be transferred?

Whatever the answer to these questions, it needs to be in this article. Or at least a link to where the answer is. Jules LT 21:55, 30 September 2005 (UTC)

I think the silence you hear is the sound of many people scratching their heads. Yes, the 2nd law has lots of empirical validation, and for most laws of physics this is the most we can ever hope for. In physics, it is usually impossible to prove anything - the most you can hope for is to try and fail to disprove something. But the 2nd law is unusual that way - because it is a macroscopic statistical property of the microscopic laws of physics, one might hope to at least prove mathematically that it follows from our current understanding of the microscopic laws of physics. But, I don't know if anyone has managed to do this yet - quite possibly, nobody has. If anyone reading this knows of a proof that the 2nd law is implied by our current microscopic models, please post that information here. Thanks. Jules - if nobody posts such a proof here, its probably b/c no readers know of one.

Jules - to address specific bullets, the best I've found for your first question is a precise description of the 2nd law in the form of equations that I'd rather not post. But, I have not found proof. For the second bullet, the answer is of course no. When your muscle cells metabolize sugar with oxygen, they convert chemical energy directly into mechanical energy without ever functioning as a heat engine. But perhaps you mean to ask if this is the only way we can convert heat into another form of energy? In some abstract sense the answer might be yes, but keep in mind that heat transfer can take many forms - for example, hot objects glow due to blackbody radiation, converting their heat energy into light - so you might consider this a sort of conversion of heat energy into another form of energy. For the third bullet, the answer I think is that this is not a useful way of thinking about it.

Thanks a lot. That explains much. Then I shall consider it something most probably and often but not necessarily true, like "the speed of light is a constant" or gravity. Maybe we could insert a phrase like "Like all physics laws, the 2nd law of thermodynamics is generally believed to be true because it was able to make accurate predictions throughout its use, but it hasn't been proved as such and it is not known exactly why it is true." Jules LT 13:55, 3 October 2005 (UTC)

Glad to help. "...most probably and often but not necessarily true..." you must be a mathematician. Technically, yes - in physics, we don't actually know anything for certain - heck, we might be brains living in a vat, and maybe the real universe is actually eight-dimensional. Or maybe the world is as we see most of the time, including the law of gravity - except that once every eight million years all rocks of a specific shade of orange will fall upwards for a few seconds. But as hunches go, this seems like a pretty safe one. (Granted - I believe in our current model of gravity more than our current model of entropy, only because entropy is a relatively new concept, but I don't advocate putting that disclaimer in the main article.) Also note: although I can't personally say that anyone has yet derived the 'proof' that I described, I also can't say that they haven't, and I'm not an expert in this topic. Also note: such proofs are rare in physics, yet our microwave ovens work pretty well. -- User:Bmord

Kooks hawking books in Wiki articles

In perusing the archive I was disturbed that a blatant plug for a self published book of New Age, crank physics/metaphysics - complete with a link to the author's webpage where the book is hawked - was able to survive in the article unchallenged until until September 28th, 2005 (I won't further promote the book by repeating the name and title - suffice it to say it was in the section of the article entitled 'Other'). It is disturbing to think that such a blatant and cranky product placement could have gone unchallenged for so long. It makes one wonder how many similar instances of this sort of mischief there might be here at Wikipedia. WikipediaEditor 19:23, 1 October 2005 (UTC)

Let's start with the beginning

quote from the article:

The second law of thermodynamics is a consequence of the first law of thermodynamics (ie., energy is conserved) and the fact that the universe is expanding.

Just curious, how is the fluctuation-dissipation theorem related to the expansion of the universe? There must have been something I missed, because with the way the article is written, if I believe in everything that's in there, then I believe something's going to happen to fluctuation-dissipation theorem the day the universe stops expanding. Oh no, I know, the day where stops expanding, fluctuation-dissipation theorem will revert so that evolution will become proven and creationnism will become forbidden by the 2nd law arf arf arf!

Not to mention broken glasses would start jumping on tables.

No seriously, I disagree with that statement on the expansion of the universe and the 2nd law, on the basis that Hawking says he has been convinced of the contrary, in his book "A brief history of time." I don't think we should disregard such authorized scientific authority, unless someone can prove this statement for good.ThorinMuglindir 23:04, 31 October 2005 (UTC)

Deletion of part related to universe collapse

ThorinMuglindir 00:50, 2 November 2005 (UTC)

I have deleted the following part of the article:

"Since the universe is tending towards a greater entropy (expanding over time), all work (see Mechanical work) processes within the universe also tend towards a greater entropy. The second law of thermodynamics is a consequence of the first law of thermodynamics (ie., energy is conserved) and the fact that the universe is expanding."

I justify the deletion with the following quote from Stephen Hawking:

"At first, I believed that disorder would decrease when the universe recollapsed. This was because I thought that the universe had to return to a smooth and ordered state when it became small again. This would mean that the contracting phase would be like the time reverse of the expanding phase. People in the contracting phase would live their lives backward: they would die before they were born and get younger as the universe contracted.

This idea is attractive because it would mean a nice symmetry between the expanding and contracting phases. However, one cannot adopt it on its own, independent of other ideas about the universe. The question is: is it implied by the no boundary condition, or is it inconsistent with that condition? As I said, I thought at first that the no boundary condition did indeed imply that disorder would decrease in the contracting phase. I was misled partly by the analogy with the surface of the earth. If one took the beginning of the universe to correspond to the North Pole, then the end of the universe should be similar to the beginning, just as the South Pole is similar to the North. However, the North and South Poles correspond to the beginning and end of the universe in imaginary time. The beginning and end in real time can be very different from each other. I was also misled by work I had done on a simple model of the universe in which the collapsing phase looked like the time reverse of the expanding phase. However, a colleague of mine, Don Page, of Penn State University, pointed out that the no boundary condition did not require the contracting phase necessarily to be the time reverse of the expanding phase. Further, one of my students, Raymond Laflamme, found that in a slightly more complicated model, the collapse of the universe was very different from the expansion. I realized that I had made a mistake: the no boundary condition implied that disorder would in fact continue to increase during the contraction. The thermodynamic and psychological arrows of time would not reverse when the universe begins to recontract, or inside black holes."

Emphasis mineThorinMuglindir 00:50, 2 November 2005 (UTC)

I demand you do not restore this part or add some equivalent affirmation, unless you can back up your claims with a quotation from a more authorized source than this one.ThorinMuglindir 00:50, 2 November 2005 (UTC)

Discussion of deletion

This sub-section is for discussion of the deletion of the part relative to the collapse of the universe.ThorinMuglindir 00:50, 2 November 2005 (UTC)

I agree with the deletion. My Stat Mech textbook (Fundamentals of Statistical and Thermal Physics, McGraw-Hill) describes the 2nd law as applying to all closed systems. From this I conclude that it applies also to closed systems that are not expanding - most of their examples are of non-expanding systems. I removed something similar before, but I guess someone added it back in - I agree it should not be added again. Bmord 18:27, 5 November 2005 (UTC)

Factual accuracy flag (Fluctuation Theorem)

I have flagged this article for lack of factual accuracy. I demand to be presented a proof that the fluctuation-dissipation theorem can be used to prove the second law of thermodynamics. I contest the factual accuracy of this assertion on the basis that the demonstration of the fluctuation dissipation theorem rests on hypotheses of a system close to equilibrium. The existence of thermodynamic equilibrium is a consequence of the second law.ThorinMuglindir 00:50, 2 November 2005 (UTC)

I demand to be shown a demonstration of the fluctuation dissipation theorem that doesn't rest on an hypothesis that stems from the second law of thermodynamics.ThorinMuglindir 00:50, 2 November 2005 (UTC)

Note the entropy production fluctuation theorem (FT) is not the same thing as the fluctuation dissipation theorem. The FT does apply to non-equilibrium systems, under quite widely-applicable conditions. I'm still working through exactly what it claims; but I think it says that if (on an ensemble average) the coarse-grained entropy is expected to increase, there is a simple formula for the expected probability distribution of the actual increase (if certain conditions are met on the presence of time-reversed paths in the ensemble).

Like I said, I'm still working my way through it, but you might also like to look at the two papers by Dewar linked in the references of the MaxEnt thermodynamics article.

The FT is definitely important, and deserves to be treated as such. On the other hand, if you go to Fluctuation Theorem and look at 'what links here', Dennis Evans does appear to wiki-spammed it pretty thoroughly through the encyclopaedia. I think it probably does help clarify a lot about the approach to equilibrium, and about entropy production in steady-state open non-equilibrium processes. But I'm not sure that it closes the book on all the conceptual/philosophical questions quite to the extent Dennis Evans maintains. Jheald 13:49, 5 November 2005 (UTC).

okay I've taken a quick look at the FT article. Not to say I understand all of this, but in any case it appears you can not apply it to any situation, whereas the Scond law of thermodynamics applies situations that are not covered by FT (see the molecular dynamics example below).

another gripe I have is that the section is called "Derivation of the Second Law from Time Reversible Mechanics," when in fact what it does is replacing the Second law by an axiom of causality." In other words, this is not at all what is announced in the section title. The second law can only be obtained (in some particular cases) by adding an hypothesis on time-irreversibility in probabilitic descriptions to the time-reversible microscopic dynamics. ,

The article claims to be a law of physics "just as classical and quantum mechanics." There is nothing to support this claim. The thing is, the second law emerges in systems where there's absolutely no room for a causality principle. Take a molecular dynamics simulation of a gas of 1000 or 10000 weakly interacting molecules. The interaction propagates instantly from molecule to molecule, and the one and only "law of physics" to which the system is submitted is law of Newtonian mechanics with a force that derives from a potential energy. Molecular simulations only have whatever ingredients you put in them, so that there's no such thing as an "Axiom of causality" in this system. Start the system in a low entropy state, for examples give the same speed to every molecule. You'll see that the system undergoes a process of thermalisation and the speeds of the molecules end up distributed very close to the Maxwell-Boltzmann distribution, corresponding to the maximum of entropy. FT can not help us in this case, because that's not the conditions in which its hypotheses work (or am I wrong here?). You could also use this simulation in other conditions to test the predictions of FT. I'm not sure, but maybe FT would be proven to be true, or not. But in that case that couldn't be a consequence of this Axiom of causality that the article speaks about, because it's not there in the simulation.

don't get me wrong, I'm not saying FT is bullshit. I'm not sure either it is valuable, but if it is, then probably within its domain of applicability it will show more predictive power than the second law. But it does not "cover" the second law which has a wider range of applicability. Since thermalisation seems to appear in molecular dynamics simulations that have only very simple, time-reversible interactions between molecules, the mainstream opinion in physics is that the second law is not a law of nature, but an emergent property in any probabilistic attempt at describing a deterministic system with a large number of degrees of freedom (and a time-reversible dynamics in the exact description). Which would explain why information theory also uses entropy. And also, it would mean there is no need for a time irreversible law of physics for entropy to exist.

Okay, I think I've got my head round what's going on now. A good paper to look at is Carberry et al, Physical Review Letters 92(14) 140601 (9 April 2004). This is basically an experimentalist paper, and it's a short 4-page PRL, so it focusses on an experimental set-up, and the (impressive) experimental results; and instead of lots of maths, there's a rather more friendly general-terms pictorial explanation of what the FT is about. (Note that IMO I think the labels dV and dV* should be swapped over in Fig 1).

So here is my interpretation.

The key fix is the same as in Boltzmann's H-theorem (particularly quantum mechanical versions), namely that in effect you are replacing a deterministic 1->1 evolution with a (time-symmetric) Markovian many->many mixing. This could happen either through regularly coarse-graining the probability distribution in phase-space; or by putting the system in contact with a reservoir (which you are effectively doing with a thermostatted system), and saying you can ignore (ie coarse grain over) correlations between the state of the reservoir and the state of the rest of the system.

So that's why there is information loss, and the (ensemble average) entropy increases -- typical behaviour for a Markov system.

Time symmetry

But the set-up is time symmetric (because the Markov matrix is time symmetric), so just like Boltzmann in 1877, we can also run the whole thing backwards in time, predict the past from the present; and just like Boltzmann, we find the entropy also increases as we run the model backwards: the model tells us that the present most likely arose as a spontaneous fluctuation from a higher-entropy past. We know that actually the immediate past was even lower entropy. So, as discussed on the MaxEnt thermodynamics page, from this wrong prediction, we should infer that there is therefore important information missing in our set-up of the problem, for example prior knowledge that we should expect particularly low-entropy initial conditions at earlier time.

The fluctuation theorem comes out, if we set up a non-equilibrium extended-time Gibbsian ensemble to model the system: we impose a set of expectation values as constraints, and then maximise Shannon entropy. (Again, see the MaxEnt thermodynamics page, the Brownian motion example in the Gull paper there, and then the Dewar papers). It turns out that if the constraint variables are odd (ie change sign) under time-reversal (eg fluxes), we can indeed rapidly extract the fluctuation theorem result for the observed thermodynamic entropy, pr(Delta S = d)/pr(Delta S = -d) = exp(d).

The FT therefore quantifies Boltzmann's statement that his H-theorem only holds probabilistically. It clarifies how the scope for fluctuations increases as the system becomes smaller and the time becomes shorter. And it is very pretty. Also, it makes everything more concrete, which is a benefit that should not be underestimated. And it gives you a sort of "extreme value distribution" on the possibility of the entropy actually fluctuating down. But at the end of the day, AFAICS it doesn't really change the conceptual/philosophical position -- you can have entropy increasing, if you accept the coarse-graining that makes the H-theorem work for the ensemble average. However, it is an assumption that the coarse-graining isn't getting rid of any 'interesting' information; if that assumption goes wrong, you may get a surprise. Jheald 21:51, 9 November 2005 (UTC)

I just have time to write a couple words: here my gripe is not on FT itself, but on the claim that it proves the second law.ThorinMuglindir 10:19, 11 November 2005 (UTC)

OK sorry I've been trapped offline for a few days. Within a couple of days, I'll edit the article and remove the flag I had put. Basically I think it will be more accurate to describe the fluctuation theorem as precising and expanding the second law rather than as proving it.ThorinMuglindir 14:08, 15 November 2005 (UTC)

Seshadri

This is a bit of a change of subject, sorry, but i dont know where else to place my question--i was reading a book on a fairly unrelated topic when i came across a refrence to C. V. Sheshadari apparently and Indian physicist who rejects the second law because it is "ethnocentric" and therefore unscientific, but i have been unable to find any argument that goes deeper than that and i was just wondering if any of you guys were familar with and willing to quote the whole thing to a layman. thanks.

The physicist Eugene Wigner is said to have said that "entropy is an anthromorphic concept", meaning that entropy is a property of the models we choose to describe reality, rather than of the fundamental microscopically deterministic dynamics itself. But I haven't heard of Sheshadari (and neither it seems has Google), so I can't say where he's coming from with his comment. -- Jheald 10:11, 15 November 2005 (UTC)

I've now found some discussions: [1] [2] [3] [4].

Note that the man's name was spelt "Seshadri", though S and Sh are often pretty interchangeable in names in Indian English. He lived 1930-1995, and was an outstanding researcher on what is now sometimes called "appropriate technology". It seems his objection here was to how "scientific" notions and definitions can drive out other culturally or economically valuable ideas. Thus the linear time of physics can drive out a traditional spiritual idea of circular time, based on the cycles of the seasons. Or the notion of thermodynamic efficiency can suppress other criteria for efficiency, which may be more relevant socially, or in terms of sustainability, or at a local practical level.

I can't say that I can see anything particularly ethnocentric in a mathematical model explaining why an ice-cube melts. So Seshadri was perhaps exaggerating his language for impact. But it's probably true that a physical theory can shape cultural perceptions and discussion far beyond its orginal area of explanation; and sometimes lead to overemphasis on what is just one particular aspect of the world. The language a physical theory is cast in can also sometimes skew the meaning or interpretation of its words in more general usage. These are things it is sometimes useful to be reminded of, and to be aware of. -- Jheald 11:12, 15 November 2005 (UTC)