Talk:Hysteresis

Basic definition of hysteresis is in hieroglyphs

The first sentence uses the terms

• path-dependence
• rate-independent memory

which as a general reader I have no clue what they are.

Can someone who knows the subject write a definition that is more understandable to a general audience?

Federico Grigio, alias Nahraana (talk) 18:20, 20 March 2008 (UTC)

Seconded. It's a difficult paragraph to digest for someone brand new to the field. Noxxeexxon (talk) 17:46, 22 September 2011 (UTC)

I've just looked at a half-dozen definitions - how's this [1]? I'm finding it difficult to phrase so that we don't talk about the rate of change with respect to time - it's not a differntiator or a high-pass filter. I thought working in the rubber band in the lead woudl be a good physical model, although I doubt many people ever notice that a rubber band stays longer the first time you stretch it. I'd like to mention the idea of "stickyness" in the lead, too. --Wtshymanski (talk) 19:13, 22 September 2011 (UTC)

I think you were headed in the right direction, Wyshymanski, but in my opinion the whole lead section needed major surgery to eliminate unnecessary terminology and a lot of redundancy. So I operated. RockMagnetist (talk) 23:55, 22 September 2011 (UTC)

Mmm, don't care for the results, nor for my last revisions either. "Memory" has absolutely the wrong connotations, especially for a reader sitting in front of a box with mumblety-mumble gigabytes of "memory". A path is a beaten down trail between the trees, or so may our reader think. What "path" are we talking about? And the lag is not a *time* lag; "lag" and "delay" imply time, and it's not necessarily anything to do with time. --01:51, 23 September 2011 (UTC)

From "Physics of Baseball& Softball" by Rod Cross, through the magic that is Google Books:

Hysteresis refers to the fact that different graphs of force vs. compression are obtained depending on whether the force is increasing or decreasing. A graph of force vs. compression ... for a metal spring is a straight line, and it is the same regardless of whether the force is increasing or decreasing. A graph of force vs. compression for a baseball...is a curved line and its shape does depend on whether the force is increasing or decreasing."

This is closer to what we need here, but has too much "whether" in it. --Wtshymanski (talk) 02:01, 23 September 2011 (UTC)

The problem is, talking about whether some input is increasing or decreasing implies that only the trend matters, when in fact a particular set of extrema is often what determines the output. I think "memory" has exactly the right connotations, because computer memory is based on hysteresis! RockMagnetist (talk) 02:38, 23 September 2011 (UTC)

You can make little BH loops, or bigger BH loops...but they are still loops even for small values of H. It's not the extrema that make hysteresis,its absolutely the history of the dependent variable - that's what the original, correct, but opaque lead meant by "path dependent". A flip flop is not a good model for hysteresis. The key element is that you don't get a single curve of effect vs. cause but instead varying results depending on the direction of change. --Wtshymanski (talk) 13:26, 23 September 2011 (UTC)

For an example where the trend doesn't matter, see the Stoner–Wohlfarth model, the main model for single-domain magnets (as are used in magnetic tapes, for example): the change in magnetization is reversible except at jumps. For what I mean by "a particular set of extrema", see the book by Mayergoyz. But we're getting off the topic of the lead section. I think my current revision is correct and a lot simpler than the one that Nahraana was complaining about. RockMagnetist (talk) 15:37, 23 September 2011 (UTC)

Consider Revising Or Replacing The Figure For Elastic Hysteresis Of A Rubber Band

The associated section describes the unloading and loading of weights attached to an "idealized" rubber band. Intuitively, as the rubber band is loaded, its length will extend and, as its length extends, its elasticity will decrease. As the elasticity of the rubber band decreases, the rate at which its length increases with additional loads likewise decreases. One would, therefore, expect, in the aforesaid figure, that the Force-Extension curve of the loading phase to approach a limiting Extension value. As the load or Force exerted on the band increases, the Extension will increase, eventually approaching, but never exceeding that limiting value. The Force-Extension curve should, therefore, eventually inflect upward. This is not depicted in the figure. The unloading phase would occur in an analogous manner.

The curve should resemble this:

http://www.revisionworld.co.uk/files/strain_33.gif —Preceding unsigned comment added by Atlasfugged (talk • contribs) 06:05, 10 October 2010 (UTC)

I agree. I propose that the figure be replaced so it provides a better graphical description.George Rodney Maruri Game (talk) 18:07, 7 November 2010 (UTC)

I can't remember whether this has any bearing on the matter, but the graph currently in the article is for Force against Extension, and the one linked above is for Tensile Stress against Tensile Strain. I recall that there are differences between the two types of graph, but I do not recall if there are differences between shapes of the curves. Viola16 (talk) 11:45, 21 November 2010 (UTC)

That's a good point about the axes. Stress, as I know it, is somewhat like Force / Area. Strain is somewhat like Length / Initial length. So the graphs appear at firs to be describing the same things. Of course, true vs engineering stress/strain should be specified, as this difference may influence the shape of the loading curves. —Preceding unsigned comment added by 129.138.44.221 (talk) 21:21, 22 November 2010 (UTC)

Force vs Extension is the same thing as stress vs Strain, except it is normalized differently. Area is assumed to be constant for engineering strain, so Stress=Force/Area represents the same thing as Force. The same goes for Strain=Extension/OriginalLength. OriginalLength is a constant and therefore the titles of the graph are irrelevant. The real question becomes what level of knowledge should be required for the page. Despite being an engineer, I'd leave it as is and go with Force vs Extension. Second, the difference in the two curves that Viola16 mentioned has more to do with the specific material and loading that is applied. Both curves are not valid hysteresis loops despite them looking slightly differently. —Preceding unsigned comment added by 66.214.14.128 (talk) 05:08, 5 April 2011 (UTC)

About the relation between hysterisis and positive feedback

System with hysteresis (B < 1; B.A > 1) where the output "over-helps" the input (avalanche-like positive feedback)

The two phenomena are closely related (at least, in the area of electronic circuits). Any amplifying circuit with positive feedback having a loop gain B.A > 1 possesses hysteresis and v.v., any circuit with hysteresis is an amplifying circuit that is comprised by such a positive feedback. IMO it is impossible to separate them (to have a hysteresis without positive feedback and feedback without hysteresis); we can use positive feedback to obtain hysteresis.

A proportional (fully analog) thermostat is an amplifier (comparator) with only a "global" negative feedback (consisting of cascaded heater, an object and a thermo sensor). The comparator of the simpler bistable thermostat has in addition a "local" positive feedback that forces the transition between the two supply rails and creates the needed hysteresis. Another example: op-amp relaxation oscillator. But how does the positive feedback do this magic? How do we obtain hysteresis by applying feedback? How do we create dual-threshold circuits? How do we convert a one-threshold circuit into a two-threshold one?

Dynamic threshold. The first trick is very simple and intuitive - when the input voltage crosses the threshold in some direction the very circuit changes slightly its own threshold to the opposite direction (i.e., it subtracts voltage from the threshold that is equal to adding voltage to the input voltage). So, the output affects the threshold and do not impact on the input voltage. These circuits are implemented with differential amplifier with series positive feedback where the output is connected to the non-inverting input and the input - to the inverting input. In this arrangement, the humble loop forms the needed summing circuit in the figure (the circle with "+" inside). Examples: classic emitter-coupled transistor Schmitt trigger, op-amp inverting Schmitt trigger, etc.

Modified input voltage. The second technique is opposite - when the input voltage crosses the threshold in some direction the circuit changes slightly the very input voltage in the same direction (i.e., it directly adds voltage to the input voltage). In this case, the output affects (helps) the input voltage and do not affect the threshold. These circuits can be implemented by a single-ended amplifier with parallel positive feedback where the output and the input source are connected through resistors to the non-inverting input. Now, the two resistors form the needed summing circuit (the circle with "+" in the figure). Examples: collector-base coupled transistor Schmitt trigger, op-amp non-inverting Schmitt trigger, etc.

From the feedback view, both the techniques above are the same - systems with positive feedback that is out of control. In both the circuit, the output voltage increases the derivative (difference) input voltage of the comparator (not of the whole circuit!) by decreasing the threshold or by increasing the circuit input voltage. The threshold and memory properties are incorporated in one element (two in one:)

Two different static thresholds. In this case, the threshold and memory properties are separated. The two different thresholds are created by separate ordinary open-loop comparators (without hysteresis) that drive an RS trigger (2-input memory cell). Again, there is a positive feedback but now it is concentrated only in the memory cell. Example: 555 timer. Circuit dreamer (talk, contribs, email) 22:25, 12 November 2010 (UTC)

Nevertheless I have restored the older text because the statement about positive feedback while removing the thermostat example does not help the reader. The example is unusual in an encyclopedic article, particularly the lead, but it is about the only text on the page which tells a reader what hysteresis actually is. It needs some cleaning which I might get a chance to do later. I agree that positive feedback is involved, although I haven't thought about the issue enough lately to form an opinion on whether it is an essential component (my guess is "yes, it is", but there may well be a counter example). Regardless of that, positive feedback is a mechanism to implement hysteresis, and not a defining characteristic. Johnuniq (talk) 00:11, 13 November 2010 (UTC)

I am very glad to find this discussion here, because I found the article non-sensical. The only part of the intro that was intelligible was the bit about thermostats -- but a thermostat is the canonical example of a negative feedback loop (the increase in temperature triggers the shut off of the part of the system that increases the temperature.) I am left with the impression that either someone is badly confused that hysteresis has something to do with positive feedback, or that the role of positive feedback in hysteresis has been inadequately explained. 24.61.41.34 (talk) 04:31, 27 May 2013 (UTC)Passerby

Do "mem" elements possess hysteresis?

(the text below is copied from memristor talk)

I do not share Chua's, Ventra's and others' (including memristor) assertions about the (unconditional) existence of hysteresis in memresistive, memcapacitive and meminductive elements (see for example [2]). Hysteresis is a rate-independent phenomenon like nonlinear resistance. This means that there is no matter if we drive a hysteretic element by slow (DC) or rapidly (AC) changing input quantity; it will show different forward/backward paths (what is the definition of hysteresis) of its IV curve in both the cases. This is not true for a volatile memristor, memcapacitor and meminductor that exhibit "hysteresis" only in the case of slow changing input. If we wiggle the input rapidly, their bizarre ("pinched") hysteresis loop will become a humble straight line (for example, imagine an inert thermistor).

If we assume that volatile "mem" elements possess hysteresis, we should accept that the ordinary ("not mem") capacitors and inductors possess hysteresis as well. For example, if we drive a capacitor with low frequency AC input current, measure the voltage across it as an output and draw its "IV curve", we will probably see a "hysteresis" loop (I am not sure if it will be "pinched"; please, check it:)

It seems only nonvolatile "mem" elements (i.e., true memory elements) should possess hysteresis since their IV curve does not depend on the input rate? Please, discuss this extremely interesting topic; I would like to know if I am right. I have copied this text from memristor talk. Circuit dreamer (talk, contribs, email) 09:48, 10 April 2011 (UTC)

I hope you don't mind, but I fixed the memristor links in the above; no thoughts on the issue at the moment. Johnuniq (talk) 09:57, 10 April 2011 (UTC)

Hysteresis doesn't have to be rate independent. Consider all the examples involving lag.RockMagnetist (talk) 13:52, 11 April 2011 (UTC)

Then the humble capacitor possesses hysteresis? Circuit dreamer (talk, contribs, email) 06:51, 12 April 2011 (UTC)

I don't know whether the capacitor's behavior counts as hysteresis. On the one hand, there is a time lag, which is one definition of hysteresis. On the other, there is no net energy loss in a cycle, so there wouldn't be a loop. I don't think merely being humble disqualifies it! But magnetic hysteresis is definitely rate dependent. The slower the time variation, the smaller the loop. RockMagnetist (talk) 13:17, 13 April 2011 (UTC)

There's dielectric losses and polarization in some kinds of capacitors, which would make the voltage across the unit somewhat "path dependent" - and on a crude level, put enough voltage on a real capacitor and it goes "bang" and cannot be reversed to its initial conditions. "Ideal" capacitors, though, wouldn't display hysteresis as I understand it (they're kept in the same lab closet with the frictionless planes, the bottle of ideal gas, and the ideal voltage and current sources). --Wtshymanski (talk) 14:22, 13 April 2011 (UTC)

Many real-world capacitors show Dielectric absorption, but that's really another sort of non-ideal behavior separate from hysteresis. As for time lag and energy loss, an ideal opamp with positive feedback has neither. Magnetic hysteresis is an important subset of hysteresis. but we need to avoid definitions that don't apply to other kinds of hysteresis. Guy Macon (talk) 16:53, 13 April 2011 (UTC)

Gymacon, you seem to think that I am arguing for a restrictive definition, but it is just the reverse. I am saying that we shouldn't restrict the definition of hysteresis to rate-independent phenomena because that would leave out magnetic hysteresis. RockMagnetist (talk) 19:07, 13 April 2011 (UTC)

Generality

Hysteresis is a very general phenomena. It seems that all fields should be treated equally here, not dismissed with "and also's". Certainly, the rest of the article acknowledges this (though the citation's are too sparse), but the introduction should be more universal also.— Preceding unsigned comment added by 146.186.131.40 (talk • contribs) 19:02, 30 March 2012 (UTC)

References

The first reference (http://www.ramehart.com/goniometers/contactangle.htm) has been moved to http://www.ramehart.com/contactangle.htm

I took care of it.

— Preceding unsigned comment added by Marvin W. Hile (talk • contribs) 14:42, 29 October 2012 (UTC)

Elastic Hysteresis (due to plasticity)

In the section on elastic hysteresis, it says, "In the elastic hysteresis of rubber, the area in the centre of a hysteresis loop is the energy dissipated due to material plasticity." How can this be caused by plasticity when there is no permanent deformation? And if this is incorrect, what is the correct name for the property which results in energy dissipation due to internal friction type losses during elastic deformation? 193.52.102.13 (talk) 18:22, 28 January 2013 (UTC)

Water table / rainfall hysteresis in Hydrogeology

I lack the technical expertise to add this topic, but as an amateur I am pretty certain the level of the water table (measured below a nominal ground level datum point) if plotted against the local rainfall will show a rate-dependent hysteresis effect. The water table falls during dry weather and continues to do so for some hours / days after there is significant rain. Similarly it continues to rise for some time after the rain stops. Would someone like to comment on this observation? I realise that there are other factors in play such as air temperature, evaporation, other sources of water and so on. --BletchleyPark (talk) 00:10, 2 August 2013 (UTC)

Thermostats are negative feedback, not positive

If a thermostat had positive feedback, the temperature would "run away," overheating more and more, or overcooling more and more. Thermostats are an example of negative feedback systems. 129.6.57.132 (talk) 17:28, 7 November 2013 (UTC)

You're right. Moreover, the hysteresis effect is a property of the feedback, not a result of it. I have removed the offending statement. RockMagnetist (talk) 21:36, 7 November 2013 (UTC)

OK, but I think the comment about positive feedback was referring to the process of switching from one state to another, and that is positive feedback. Taking an air conditioner, the overall cycle is negative feedback: rise in room temperature causes cooling to switch on which opposes the initial rise. However, the point about hysteresis is that something has to jam the cooler on by switching it from "off" to "on" with the assurance that it won't swing back to "off" after running for a second. Moreover you don't want the cooler to be switched half-on when the room is a little warm. Johnuniq (talk) 22:41, 7 November 2013 (UTC)

If you're right, it would be best to make the point properly in the body of the article (with sources) before adding it back in the lead. RockMagnetist (talk) 23:24, 7 November 2013 (UTC)

Elastic hysteresis diagram

Wikiversity has a student lab that confirms what you are saying. Be warned that Wikiversity research is not refereed and should not be cited on Wikipedia. --Guy vandegrift (talk) 18:27, 13 April 2015 (UTC)

An IP editor has claimed that the diagram in Hysteresis#Elastic hysteresis is incorrect: "The diagram should be a steep gradient followed by less steep and then steep." Does anyone know if that is true? I found one diagram from a publication that looked like the one in this article, but it is just a schematic. A citation would be useful. RockMagnetist (talk) 18:00, 11 April 2014 (UTC)

I formally tagged the image itself (commons:File:Elastic Hysteresis.svg), including several links that support the IP's claim (the IP had also left a note in the image-description there) and a possible origin of the confusion. And I left a note for the uploader of the image at commons:User talk:Tiger66, but that account appears inactive on all wikis since December 2012. DMacks (talk) 18:33, 11 April 2014 (UTC)

Uploader agreed with the problem and uploaded a replacement image that resolves it, so I'm going to un-tag the article. DMacks (talk) 02:12, 14 April 2014 (UTC)

:::That diagram looks like the same one with a different vertical scale. I think the other editor was saying that the curve should have negative curvature at first and then positive curvature - as in this image. RockMagnetist (talk) 14:52, 14 April 2014 (UTC) Sorry, I needed to refresh the page before I could see the new image. RockMagnetist (talk) 14:57, 14 April 2014 (UTC)

If only there were some term to describe a lag between a changed input to a complex system and the resulting output we see! DMacks (talk) 15:32, 14 April 2014 (UTC)

It's on the tip of my tongue. RockMagnetist (talk) 16:04, 14 April 2014 (UTC)

File:Elastic_Hysteresis.svg does did seem wrong to me. See image posted to right. I placed it ahead of all discussion so it would fit nicely in this section.[User:Guy vandegrift|Guy vandegrift]] (talk) 15:50, 13 April 2015 (UTC)

Also, I placed the link to this diagram in External Links at the bottom of your article to conform to WP standard practice on sisterlinks. I am not asking you to move the link up to the section on mechanical hysteresis, but won't complain if you do.--Guy vandegrift (talk) 18:27, 13 April 2015 (UTC)

• See Wikiversity:Physics and Astronomy Labs/Hooke's law and Young's modulus

---Guy vandegrift (talk) 16:53, 14 April 2015 (UTC)

Magnetic hysteresis (Section 5.1)

Section 5, Hysteresis in materials, subsection 5.1, Magnetic hysteresis, seems pretty clear to a layman until the end of the second paragraph, reproduced just below:

"...If the magnetic field is now reduced monotonically, M follows a different curve. At zero field strength, the magnetization is offset from the origin by an amount called the remanence. If the H-M relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop called the main loop. The width of the middle section is twice the coercivity of the material.[16]"

The phrase "...plotted for all strengths of a magnetic field..." probably means for all strengths, both in the original direction and also in the opposite direction. But this is not clear because the previous sentence stops at "...zero field strength..." which in the diagram is the y-axis. The part of the upper curve to the left of the y-axis is not explicitly explained, either in the text or in the diagram. Moreover, even less clear is the lower curve in the diagram which is not mentioned at all, much less explained or labelled, which includes its not having any directional arrows. Wikifan2744 (talk) 20:20, 20 October 2014 (UTC)

Here is a correction and addition to what I say above. Contrary to what I said, yes, the lower curve is mentioned. But it is not labelled with arrows nor discussed. Further, both the short middle curve and the right side of the upper curve have arrows going in both directions, quite confusing, even to someone who already knows a little bit about the subject.

In addition, earlier in the part of the second paragraph quoted above, it says, "...If the magnetic field is now reduced monotonically, M follows a different curve....." Does that mean actively reduced? If so, what happens if the magnetic field is merely turned off? Which curve is followed in each case? Does the part of the upper curve to the left of the y-axis mean that this "monotonic" reduction includes suddenly reversing the direction of the applied magnetic field? Are the curves the same regardless of how rapidly the magnetic field is changed or reversed or cycled? Under what circumstances does the lower curve come into the process? All of these are matters surely perplexing to a novice; and, as I say above, they are even quite confusing to someone who already knows a little bit about the subject. Wikifan2744 (talk) 22:49, 20 October 2014 (UTC)

I don't like the new lede sentence.

The new lede sentence reads:

• Hysteresis is the time-based dependence of a system's output on current and past inputs.

I prefer the original lede, but think it should be revised:

• Hysteresis is the dependence of the output of a system not only on its current input, but also on its history of past inputs.

The editor claims that the original lede violates gramatical conventions, and I am relatively unsophisticated in such matters. My concern is with readers who have no idea what hysteresis is. One problem, is that the word "current" might lead the reader to think of electrical current. I also think a brief definition is not in order here. Instead, we need more of an explanation. I reverted the recent edit, and the editor reverted. The present lede is acceptable, so I will not revert. But if any editor does not like the lede, please change it. I will continue to watch this page, but will take no action until someone else either edits or adds a comment to this section. I am not always right in such matters, and I know it.--Guy vandegrift (talk) 16:01, 13 April 2015 (UTC)

I think a simple change from "current" to "present" will do it. RockMagnetist(talk) 15:36, 3 September 2015 (UTC)

See discussion under § Confusing? below. —Coconutporkpie (talk) 00:29, 18 September 2016 (UTC)

Confusing?

@Coconutporkpie: You have tagged the lead as confusing, and in your edit summary you say "wording of lead section is vague and does not explain concept in everyday terms". Could you please clarify? I'm not seeing the vagueness, and as for the language, the most difficult word I see in the first paragraph is "dependence". RockMagnetist(talk) 13:54, 15 September 2016 (UTC)

The given definition of "time-based dependence of a system's output on present and past inputs" is vague, as is the following statement "the history affects the value of an internal state" — history of what? Internal state of what? The essential concepts of system, input, and output are not defined, even briefly, for the average reader. Time-based dependence could mean anything.

These concepts may be trivial for some readers with a technical background, but according to What Wikipedia is not, "A Wikipedia article should not be presented on the assumption that the reader is well versed in the topic's field. Introductory language in the lead (and also maybe the initial sections) of the article should be written in plain terms and concepts that can be understood by any literate reader of Wikipedia". —Coconutporkpie (talk) 00:21, 18 September 2016 (UTC)

What this article calls time-based dependence is more clearly and specifically explained by Princeton's WordNet as "the lagging of an effect behind its cause". Collins English Dictionary specifies that the context is physics. Both emphasize the application to magnetism in their definitions. —Coconutporkpie (talk) 00:43, 19 September 2016 (UTC)

Reading beyond the lead section, much of the article is written in a very technical style, heavy on mathematical equations with little introduction for laypersons, particularly under Hysteresis § Types. Technical terms appearing in the text without explanation for the average, non-specialist reader include "theory of nonlinear operators", "sinusoidal input and output ", "phase lag", "linear systems", "frequency domain", "complex generalized susceptibility", "mathematically equivalent to a transfer function", "mesoporosity", "adsorption isotherms", "wetting adsorbate", "matric potential", etc. Maybe Template:Technical would be a better tag for the article until the problem is fixed. —Coconutporkpie (talk) 12:12, 19 September 2016 (UTC)

I added that template here. —Coconutporkpie (talk) 13:09, 12 November 2016 (UTC)

O.k., now I see the problem, but I don't think the dictionary definitions are adequate because they don't address the breadth of the subject. I think the key is to move quickly to a specific example, and magnetism is a good choice for that. I'll take a crack at it. RockMagnetist(talk) 17:55, 12 November 2016 (UTC)

"Sinusoidal input and output" shouldn't cause much confusion, since the equations follow immediately. I added a link to sine wave. RockMagnetist(talk) 17:28, 13 November 2016 (UTC)

Hysteresis curve

The phrase "hysteresis curve" redirects to this page, but the phrase does not exist anywhere in the article. Could someone please add a description, or some kind of correction/explanation if the phrase is somehow discouraged or nonsensical? 72.214.208.2 (talk) 15:26, 23 March 2017 (UTC)

The article pretty quickly devolves from the general idea of this topic to specific examples, and only used the term "curve" in relation to each example. I added the more general phrase with a general description to the lede. DMacks (talk) 15:43, 23 March 2017 (UTC)

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Use in sociology

Hysteresis is a key concept in the sociology of Pierre Bourdieu. The concept is necessary for Bourdieu because his key concept of habitus implies a certain delay in adapting to changes in the field. For example, if a factory worker loses their job it may take them some time to be retrained in a new technology. Someone who takes up the piano as a teenager is at a disadvantage by comparison who a person who has had lessons since they were a young child. It may be possible to catch up, but in both examples the person is at a disadvantage in the social field because of their previous experience. Source: Cheryl Hardy, Hysteresis, in Michael Grenfell ed. Pierre Bourdieu: Key Concepts (2008). — Preceding unsigned comment added by 70.50.141.229 (talk) 03:15, 12 November 2017 (UTC)

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Matching Relay and Solenoid

The text notes that a latching relay may use a solenoid to hold the relay at a position after power is removed, however many latching relays use a magnet to hold the relay's position after power is removed, then power is used to overcome the relay coil's hysteresis and the magnet holding the relay's position. So the ext is a bit off, many latching relays utilize magnets, not solenoids. SoftwareThing (talk) 17:37, 30 August 2018 (UTC)

Minor Errors

The first sentence in section "Types" ends with a Greek letter. This (exact) letter does not appear anywhere else in the document. It either needs to be altered or removed. I'm not familiar with the physics (or I would fix it myself), but it looks like it should be a capital phi. GregJ77 (talk) 13:29, 8 May 2019 (UTC)

@GregJ77: Thanks for pointing this out. It's actually a formatting issue - the inline phi looks different from the display phi. I have tweaked the standalone equation and they are still different, but I hope it's now clear they are the same letter. RockMagnetist(talk) 14:46, 8 May 2019 (UTC)

Overbroad definition

The lead defines hysteresis simply as system dependence on history. I'm no expert here, but as I read into the topic it seems that hysteresis usually means something much more specific. Morris (2011) points to "two key aspects of hysteresis that are still regarded as characteristic today: “lagging” and rate-independence" - this makes it a far more specific system property that simple dependence on history. Kyle MoJo (talk) 04:38, 8 April 2020 (UTC)

Conflicting statements in definition

The first sentence says "Hysteresis is the dependence of the state of a system on its history." and the first sentence of the last paragraph of the intro says "Systems with hysteresis are nonlinear". Those are conflicting statements. Linear systems' state can definitely depend on history. From where I come (control systems) hysteresis is a phenomenon when a system's static characteristics depend on history, no just its dynamic state. Some ambiguity may come from the definition of "state" - for me it's the current, momentary value state. Other fields may have a different point of view, but those two sentences are definitely conflicting. Petar Petrov Donchev (talk) 06:44, 22 January 2021 (UTC)