Talk:Non-equilibrium thermodynamics

Discrepancy between spelling of article and category title resolved
I noticed that there was a discrepancy between the title of the article &mdash; spelt "Non-equilibrium thermodynamics" &mdash; and the spelling of the category, which was spelt "Nonequilibrium thermodynamics".

I decided this was worth resolving. IMO the spelling with the hyphen is more clear so I decided to go with that one, and I have done the following:


 * All sub-categories and articles in the category of Category:Nonequilibrium thermodynamics have been changed so they now belong to Category:Non-equilibrium thermodynamics.
 * Category:Nonequilibrium thermodynamics has had all its categories removed (so it will not show up any more as one descends the hierarchy of categories); the page has been replaced with a redirect to Category:Non-equilibrium thermodynamics.

I did this by hand, a pain in the ass, so if anybody knows of a method to quickly make such changes in future, do let me know. Not that I'm planning on doing such things on a regular basis. :-)

Feel free to flame, abuse and otherwise censure me if you feel what I've done was out of line.

I would suggest that we put Category:Nonequilibrium thermodynamics up for deletion but thought I'd leave it as a redirect for now in case anyone really, really wants it back. Best wishes, &mdash; WebDrake 18:29, 17 October 2005 (UTC)

Example of non-equilibrium system
The Belousov-Zhabotinsky reaction is no more an example of a non-equilibrium chemical system than any other reaction. All reactions start at a non-equilibrium state and move to equilibrium as entropy is produced.

While most relatively simple reactions describe a monotonous concentration = f(time) path to equilibrium, the Belousov-Zhabotinsky reaction belongs to a kind of reactions that have autocatalytic steps, which makes some intermediate components concentrations oscillate as the reaction proceeds to equilibrium. The oscillations are damped until, at equilibrium, they disappear and all concentrations become stationary.

The introduction to the article states correctly that non-equilibrium systems are abundant and all-around us. Systems like a hurricane, a working combustion engine, a ping-pong ball suspended in an air jet, a flying aeroplane or a living cell are all examples of non-equilibrium systems. All the best, Pilha de Areia (talk) 10:51, 26 November 2008 (UTC)

Lacking accuracy
Could equilibrium thermodynamics be generally characterised as lacking the accuracy of non-equilibrium thermodynamics ?

(or, to put it another way, Thermodynamics lacks the precision required for understanding many physical systems ??)

if so, should the article make some mention of this situation. so that the lay reader would be less confused by the distinctions equilibrium and non-equilibrium and hopefully see that Thermodynamics often produces results lacking accuracy. 79.76.136.100 (talk) 19:44, 13 February 2009 (UTC)

I do not think that equilibrium thermodynamics could be generally characterised as lacking the accuracy of non-equilibrium thermodynamics. It is of course true that inaccuracy will result from trying to apply equilibrium thermodynamics to non-equilibrium problems. The reason that people do the latter is that it is much much much harder to apply non-equiliibrium thermodynamics to non-equilibrium problems than to apply equilibrium thermodynamics to equilibrium problems.Chjoaygame (talk) 00:52, 20 August 2009 (UTC)

Maximum Entropy Production and Prigogine's Theorem of Minimum Entropy Production Sections
The name for these sections had been THE Principle of Maximum Rate of Entropy Production and Principle of Minimum Rate of Entropy Production.... There is no "THE: Principle of...Maximum...there are historical several authors who have put out theories or postulates about maxium entropy production with different names and which are not equivalent, Swenson, for example put out a "Principle of Maximum Entropy Production" in 1988 and the stated what he called "The Law of Maximum Entropy Production" beginning in 1989 (of which there is a separate Wikipedia article). Dewar recently put out a principle of maxiium entropy production which has been shown to be invalid but it was a different principle. So this section which should touch on all these should not be named "THE". I furnished the basic details on these. Regaarding the title of the next section, there is a name for a principle here but it is not as given previously it is as it appears now the "Theorem of Minimum Entropy Production" and belongs to Prigogine to whom it is attirbuted now in the title. I've fleshed in the details of that theorem and shown the relatnon to the previous section. This was done partly following the contribution of a previous editor who had referred people to the Wiki article on the Law of Maximum Entropy Production where he correctly noted there was a better discussion of Prigogine's theorem. But this page is where this should clearly also be because this whole page is the more general page which should cover all these things. The Law of Maximum Entropy Production page is a more specific page which is about that specific law due to Swenson. That page, which is certainly an important page, is really a detail of the larger area of study of nonequilibrium thermodynamics, so if anything discussions of other principles than Swenson's Law of Maximum Entropy Production should be referred here. —Preceding unsigned comment added by DrProbability (talk • contribs) 23:23, 24 September 2009 (UTC)
 * That comment "The name for these sections... should be referred here." was unsigned but is recorded as having been put in at 23:23, 24 Sep 2009 by DrProbability.Chjoaygame (talk) 20:21, 6 March 2010 (UTC)

Swenson's Law of Maximum Entropy Production is obviously correct
If people would but stop and think about what he has said (summarised at http://lawofmaximumentropyproduction.com/) Swenson's Law (first discussed in 1988)is intuitively obvious. The Second Law tells us entropy will increase within the constraints of the system for which there is obviously a maximum entropy state. The stable density gradient in the troposphere is one such example of a result of the Second Law process. Swenson firstly points out that Nature acts that way because unstable states (that is, states that are not maximum entropy) have unbalanced energy potentials. Entropy increasing is synonymous with unbalanced energy potentials dissipating. Those potentials may involve just kinetic energy (and that is why the Clausius "hot to cold" corollary of the Second Law applies in a horizontal plane wherein there are no changes in gravitational potential energy) though they can involve any form of internal energy. Hence a ball rolls down a slope as a result of the Second Law process of maximum entropy production. What Swenson added to the Second Law (without in any way negating that law) was the fact that the system maximizes entropy by the fastest possible route, which should be obvious to anyone with a sense of what happens in the physical world. If a warm log cabin has two windows (one almost closed and one wide open) more thermal energy will escape through the wide-open window. — Preceding unsigned comment added by 202.172.115.20 (talk) 05:48, 8 July 2017 (UTC)


 * The following paper has a simple counter-example against any entropy maximization principle . Quoting "Dissipation was discussed in the introduction of the paper. This is the variational principle that some have postulated for non-equilibrium systems, namely that the optimum state is given by either a maximum or a minimum in the rate of entropy production. For the case of heat flow, the dissipation is the heat flux divided by the temperaturegradient, which is essentially the Nusselt number. The results in Fig. 5 for a spontaneous cross roll transition show that neither the measured nor the calculated final wavenumber correspond to the maximum Nusselt number. [...] The behavior of the Nusselt number and its equivalence to the dissipation rules out any general principle for nonequilibrium systems that asserts that spontaneous transitions between states correspond to a monotonic change in the dissipation. The corollary of this is that there can be no general Principle of Extreme Dissipation for determining the optimum non-equilibrium state." The counter example is the experimentally verified and theoretically well understood case of heat dissipation creating convection rolls in fluids, and could correspond to the convection of heat through open windows. Nomenenus nescio (talk) 20:27, 16 September 2020 (UTC)


 * By your leave, Editor Nomenenus nescio, I have indented your comment as in the usual format for these pages.


 * Thank you, Editor Nomenenus nescio, for your valuable comments and edits.Chjoaygame (talk) 05:22, 18 September 2020 (UTC)


 * I have taken the liberty of making some wording changes that I intend to leave intact the substance of your valuable edit.Chjoaygame (talk) 05:31, 18 September 2020 (UTC)

added some references
Added some historical references about thermodynamics, fluid mechanics, and meteorology.Chjoaygame (talk) 02:31, 27 September 2009 (UTC)

local and integral variables
Made some alterations to clarify the nature of the variables of concern to non-equilibrium thermodynamics. It is not necessarily possible to define local macroscopic quantities for systems that are not in thermodynamic equilibrium, but when it is possible to define then, such systems can be investigated by the methods of thermodynamics. One starts with locally defined gradients and flux densities of extensive quantities as well as of intensive quantities.Chjoaygame (talk) 03:51, 27 September 2009 (UTC)

Swenson POV and balance
A single editor inserted a bunch of refs to the work of Swenson which seems to be out or proportion to prominence and acceptance in the literature, maybe even fringe.


 * That comment "A single editor ... fringe." was unsigned. It is recorded as having been put in at 17:15, 29 Sep 2009 by Nerdseeksblonde.Chjoaygame (talk) 20:21, 6 March 2010 (UTC)
 * Please remember to sign with the four tildes.Chjoaygame (talk) 21:52, 29 September 2009 (UTC)

It is time to delete the afore-mentioned paragraph on Swensonism. It is pseudo-science, politely called "fringe" in the foregoing comment.Chjoaygame (talk) 17:12, 10 April 2010 (UTC)

Second notice of time to delete the paragraph
This is a second notice that it is time to delete the afore-mentioned paragraph on Swensonism. It is pseudo-science, politely called "fringe" in the foregoing comment.Chjoaygame (talk) 23:48, 1 May 2010 (UTC)

Action of removing the Swensonist propaganda
Following the above notices, I have now removed the offending Swensonist propaganda. I think this ought to justify removing the tag at the head of the article that says that the article is of disputed neutrality.Chjoaygame (talk) 15:01, 30 June 2010 (UTC)

Time to remove NPOV tag
It seems to me that it is now time to remove the NPOV tag from this article. The reason for the tag was the presence of a bunch of Swensonist propaganda. Swensonism is pseudo-science, out of place in this article. It seems that there is no longer a defender of the Swensonist material having a place in this article. I do not see a specific procedure for removing the tag, and so I am posting this comment for that purpose.Chjoaygame (talk) 11:13, 3 July 2010 (UTC)


 * The procedure is either to discuss and see if anyone objects - you've done that - or to just remove it - I've now done that. I also removed the very old "expand" tag which didn't seem useful William M. Connolley (talk) 20:57, 14 July 2010 (UTC)

Thank you.Chjoaygame (talk) 02:00, 15 July 2010 (UTC)

Onsager 1931 (I)
I have added references to the first of Onsager's 1931 papers that orginated this subject, with special note of the important distinction that Onsager made between the rates of entropy production and of energy dissipation.Chjoaygame (talk) 23:24, 3 October 2009 (UTC)

Grinstein and Linsker 2007 detailed
I have put in a more precise statement of what Grinstein and Linsker (2007)says, and added a quote of their conclusion.Chjoaygame (talk) 10:53, 4 October 2009 (UTC)

more details of historical development of ideas of extrema of rates of energy dissipation and of entropy production
I have clarified and added more details of the historical development of ideas of extrema of rates of energy dissipation and of entropy production. Also I have re-arranged the section on these matters.Chjoaygame (talk) 01:08, 5 October 2009 (UTC)

notes on local thermodynamic equilibrium
I have added some notes on local thermodynamic equilibrium.Chjoaygame (talk) 04:06, 16 October 2009 (UTC)

"Constructal law"
Talk of "the constructal law" will be attractive to those who want to find Aristotelian telic explanations in matters where I think Aristotle himself would probably restrict himself to kinetic, material and formal explanations. I would suggest to the current Bejanist protagonist that he do not go further with his creeping insertion of this kind of teleology where it does not properly belong, no matter how much the Bejanist protagonist wishes it did.Chjoaygame (talk) 23:44, 20 December 2010 (UTC)

references to the work of Umberto Lucia
An editor 217.172.220.186 has put in a fair number of references to the work of Umberto Lucia. At page 292 of his article 'Irreversible entropy variation and the problem of the trend to equilibrium', Physica A, 376: 289-292 (2007), Lucia writes apparently uncritically about the "constructal" theory of Bejan. The work of Lucia is in the area of rational thermodynamics which is not quite the same as ordinary classical thermodynamics, rational thermodynamics being a very abstract and specialized subject. The rather grand apparently universal proposals of Lucia seem far more general than is accepted by established authorities. Though he has been publishing in this area at least since 1995, Lucia is not cited in Grandy's relatively comprehensive and authoritative 2008 book, nor in the 2008 book by Lebon, Jou, and Casas-Vázquez, nor in the 2007 discussion by Stijn Bruers, 'A discussion on maximum entropy production and information theory', ''J. Phys. A: Math. Theor.'', 40: 7441-7450, who concludes about other work; "We end this appendix by repeating that the above ideas are still very speculative". If the editor 217.172.220.186 wants to go further with his entries on Lucia's work, I think 217.172.220.186 needs to give a justification in this talk page before doing so.Chjoaygame (talk) 03:19, 26 January 2011 (UTC) — Preceding unsigned comment added by Chjoaygame (talk • contribs) 03:14, 26 January 2011 (UTC) Sorry I forgot to sign. I have now signed.Chjoaygame (talk) 03:19, 26 January 2011 (UTC)

Further editing by an editor identified as 79.24.75.132 has occurred. The further edits were reverted by editor Favonian, but it seems they eventually stood as made by 79.24.75.132. The effect is the addition of several new references to the work of Lucia. It seems that the editor 79.24.75.132 feels he is safe ad libitum to add this kind of material, though I have proposed that editor 217.172.220.186 should justify here in this talk page further additions of the same kind. What are the connections, if any, between editors 217.172.220.186 and 79.24.75.132 and Umberto Lucia?

The work of Umberto Lucia is cited here as primary source information, not secondary or tertiary reports by established authorities. According to Identifying reliable sources, "Articles should rely on secondary sources whenever possible. For example, a review article, monograph, or textbook is better than a primary research paper. When relying on primary sources, extreme caution is advised: Wikipedians should never interpret the content of primary sources for themselves. See Wikipedia:No original research." There are now more references in the present version of the article to Lucia perhaps more than to Prigogine and Grandy (I lost count).

In addition to my above note that Lucia is not cited by Grandy 2008 nor by Lebon, Jou, and Casas-Vázquez 2008, I note that Lucia is not cited in the 2006 review by Martyushev and Seleznev, which has 159 references on this specific topic.

The subject of a proposed general principle of maximum rate of entropy production as a character of stable stationary states of physical systems far from thermodynamic equilibrium is conceptually difficult and the more established authorities are not sanguine about its possibilities, though various individuals who are not recognized authorities are very enthusiastic about it.

Not only editor 217.172.220.186, but also any editor who wants to put in material about Umberto Lucia's work needs, I think, to offer very much more justification in this talk page than has been provided so far, namely nil. I am inclined now to think that it might be best to delete altogether any reference in this article to Umberto Lucia's work. It seems it was a mistake to include even the mention of his work that preceded the edits of editor 217.172.220.186 .Chjoaygame (talk) 02:53, 27 January 2011 (UTC)

New edit about the earth and Sun not appropriate at this point
There is a new edit: "Most systems found in nature are not in thermodynamic equilibrium because our planet is situated near the Sun, which produces strong temperature and photon density gradients. Non-equlibrium thermodynamic systems are typically characterized by a presence flux of matter and energy between parts of the system."

The new edit is about the singular cause of the non-equilibrium state of the earth, but what is needed here is a general statement here about systems throughout the universe. Most systems found in nature are very far from our planet and from the Sun. I think the new edit is inappropriate because it is too particular when generality is needed. I am not at this moment undoing the new edit because I suppose its author may not like me to do so, and may wish to present some reasonable argument for its appropriateness, which I would like to see. I think the author should undo his own edit.Chjoaygame (talk) 08:08, 16 February 2011 (UTC)


 * I have undone the above-quoted new edit for the reasons given above, with no reply from the new editor.Chjoaygame (talk) 03:06, 19 February 2011 (UTC)

Reasons for undoing the recent edits made by Bernhlav
Sad to say, though well-intentioned, the recent edits by Bernhlav are not right. They are based on inadequate understanding of the material and are to some degree illogical in their own terms. If Bernhalv wants to make more edits along the lines of these, it is not enough that he rely on the opinions of Lavenda 1978. He needs to read and understand De Groot and Mazur (1962) and Glansdorff and Prigogine (1971) more thoroughly before making this kind of edit. He may perhaps also benefit from reading Lebon, G., Jou, D., Casas-Vázquez, J., Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers, Springer-Verlag, Berlin, 2008, e-ISBN 9783540742524, and Kondepudi, D, Introduction to Modern Thermodynamics, Wiley, Chichester, 2008, ISBN 978-0-470-01598-8. I suggest he make separate edits for each of the different parts of the article that he works on, and that he justify each of his edits by giving well thought-out reasons for each of them in this talk page.Chjoaygame (talk) 18:09, 6 March 2011 (UTC)

It is the duty of the one who claims "not right" to point out where it is not right. "Opinions" are one thing, facts are another. There are a lot of inaccuracies in the article on non-equilibrium thermodynamics, and certain contributions are blown up out of proportion in respect to the mainstream of non-equilibrium thermodynamics. It is well-known that "local equilibrium" has no meaning macroscopically because you can't put a set of cells, all of which are in local equilibrium, into contact to form a gradient of heat or concentration or anything else. Onsager's proof of his reciprocal relations employs the principle of microscopic reversibility and so makes them applicable to fluxes that are time derivatives of extensive variables, and not heat or material fluxes. There are no extremum principles for steady states because there must be a finite thermodynamic force to maintain the system from relaxing to equilibrium. The entropy production is a first-order homogeneous function of the fluxes, and thus cannot be minimized, contrary to the Rayleigh-Onsager dissipation function, which is a second-order homogeneous function of the fluxes. I don't think I have to read Glansdorff and Prigogine because my work appears in Chapter 16. I have not seen where these points are addressed in the article. The article needs a major over-haul if it wants to convey correct information. — Preceding unsigned comment added by Bernhlav (talk • contribs) 18:02, 7 March 2011 (UTC)


 * Dear Bernhlav, Thank you for your valuable reply. I accept that I have a duty to put my case.


 * You write " I don't think I have to read Glansdorff and Prigogine because my work appears in Chapter 16." I do not see the name Bernhlav in the reference list of that book, but examining the reference list, I see the name B. Lavenda as the author of a 1970 thesis, and in Chapter 16 I see a citation of Lavenda and Nicolis (1969) which is not listed in the reference list. It is a fair guess, I think, that you are B. Lavenda, and that you are therefore citing your own research in your proposed edit. I should point out now that the Wikipedia has rules against editors' citing their own personal research, and that, on the face of it, those rules are likely to be applicable here. The rules, loosely read, prefer secondary or tertiary sources. May I refer you to WP:NOR and to WP:PRIMARY.


 * I would like to work this through with you. If the article is seriously inaccurate as you propose, then it will need major revision. A major revision will best be made, I think, cooperatively or at least systematically, and not by catch-as-catch-can multiple editing. I will value your knowledge for this purpose. I will try to engage constructively for this. It seems quite likely that you are far more expert in this area than I am. If my guess is right, and you are B. Lavenda, and have worked with Nicolis, then quite obviously your expertise is to be respected.


 * I have not closely examined the whole article, and there are many parts of it that I think are obscure and perhaps wrong, or in need of revision or better expression. Likely you are an expert who might do a lot to improve the article. Your approach seems significantly different from that taken in the article as it stands; as I understand the present article's approach, it is the commonest orthodox reading of the secondary sources; of course the orthodoxy can be wrong. Likely I was mistaken to suggest you need to read more, and if so I am sorry; I would then have been misled by the difference of your approach from that of the article as it stands.


 * Right now I think we cannot deal with everything at once. I would like to suggest we go bit by bit. I will start with some comments that may lead to a productive conversation. Otherwise perhaps you might like to proceed in some other way.


 * As I understand it, 'local thermodynamic equilibrium' refers to an approximation. The approximation refers to the case when the reactions are so slow and the gradients of local intensive variables are so small that the Maxwell-Boltzmann distribution is near enough sustained as it would be in equilibrium with the local values of the intensive variables. When the conditions are not satisfied, the approximation is not applicable, and the so-called 'classical irreversible thermodynamics' cannot deal with the problem to a useful degree of approximation. My grounds for these beliefs are in De Groot and Mazur 1962, in various works by Prigogine, and in two books by Lebon, Jou, and Casas-Vázquez 2001 and 2008. Perhaps I have misread these sources, perhaps they are mistaken in themselves. I agree that the framework of 'classical irreversible thermodynamics' is not an exact one; it is an approximation as I have just noted. I am not clear whether you think that as an approximation, 'classical irreversible thermodynamics' is hopelessly wrong, or whether you think that is a rough approximation but one that is not good enough to deserve a place in an article of this kind.


 * Consequently, I am puzzled by your statement: "It is well-known that "local equilibrium" has no meaning macroscopically because you can't put a set of cells, all of which are in local equilibrium, into contact to form a gradient of heat or concentration or anything else." I imagine a rod with one end in a hot bath and the other in a cold bath. At a steady state, the temperature gradient will be constant. Now I imagine a macroscopic procedure in which the same rod cut into segments, and each segment separately is brought to equilibrium at the temperature appropriate for its sequential place. Then I imagine the segments being put together again with the end segments in contact with the original heat baths. After a while, I imagine that this will lead gradually back to the original temperature gradient, and that the formalism of 'classical irreversible thermodynamics' will work for this. Perhaps I am mistaken here.


 * Perhaps that is enough for a start.Chjoaygame (talk) 02:59, 8 March 2011 (UTC)

Dear Chjoaygame,

That Chapter in Glansdorff and Prigogine deals with multi-stationary state transitions in homogeneous chemical systems far from equilibrium. The reference is to Nicolis and myself; Prigogine used Edelstein's scheme but it was my work he and Glansdorff were discussing. In fact, he believed that the entropy production would go up going away from equilibrium like in hydrodynamic instabilities where the formation of structure requires a larger entropy production. I showed just the opposite: the entropy production goes down when there is a transition from the thermodynamic to kinetic branches so as to regain lost stability. The transition is caused by the system's loss of stability. There is a difference between local equilibrium as used in the Chapman-Enskog method of solving Boltzmann's equation, and its use macroscopically. I believe it was Peter Landsberg who pointed in his Nature review of the Glansdorff and Prigogine book that if you have a set of cells in contact, all of which are in a state of local stable equilibrium, then you cannot get a criterion for instability by summing over all stable systems. Local equilibrium means that the entropy of each cell has the same functional dependencies as it does in equilibrium, and its stability criterion is couched in the negative semi-definite form of what Prigogine referred to as the "excess" entropy, or what Tisza called the stiffness matrix. These are the usual conditions of equilibrium thermodynamic stability. The criterion he proposed was: 1. the excess entropy cannot be positive, and 2. its time rate of change, evaluated by using the kinetic equations, is positive. Rather than being a Lyapounov criterion of sufficient stability, it consists of two separate conditions: one based on equilibrium thermodynamic considerations, which are always met because the system is in a state of local equilibrium, and the other on some kinetic form of stability. This I discuss on p. 70 of Lavenda (1978). Moreover, the assumption of local equilibrium is detrimental to Prigogine's "universal" criterion of evolution. He split the variation of the entropy production into two parts: one with respect to the fluxes and the other the forces. The former could not be shown to have a good sign, and so was discarded. The second, he claimed, was always negative definite on account of "stability with respect to diffusion." In a short note in Lettere al Nuovo Cimento in 1972 I pointed out that if local equilibrium exists, so too must the Gibbs-Duhem relation which safeguards the fact that there can be no thermodynamic potential which is a function only of intensive variables. In other words, the complete Massieu transform of the entropy is identically equal to zero. Hence d_XP, the variation of the entropy production P with respect to the thermodynamic forces, X, is identically equal to zero. So local equilibrium is something that you don't want if you are looking for conditions of stability in non-equilibrium systems, and if you not, then there is no interest at all. Have I made myself clear? I wasn't trying to give myself publicity, but when I saw a huge gap in the literature I wanted to set things a little more evenly. In fact, none of these topics appear in the article, yet lie at the heart of irreversible thermodynamics. — Preceding unsigned comment added by Bernhlav (talk • contribs) 17:54, 8 March 2011 (UTC)
 * Dear Bernhlav, Thank you for your valuable post. I am very interested to read what you write, and will try to get my head around it as quickly as I can. I am sorry that I am scheduled to have some very heavy duties over the next week and so I must ask for time to digest and respond properly. I have found myself puzzled by some of the claims in the literature, and I look forward to perhaps having some of my puzzlement dissolved by your perhaps radical thoughts.


 * In the meantime, as I read your present post, you have not directly and explicitly replied to my post of 02:59, 8 March 2011. Though my post may have been nonsense or too elementary or trivial to be of value, I would still like to have your direct and explicit response to it, if you will be so kind. Just to be sure that we are on the same page, or least in the same chapter.Chjoaygame (talk) 01:14, 9 March 2011 (UTC)


 * To be more explicit about what I am asking you to answer in the meantime: In my post above I am asking two questions. One is asking if you think the whole idea of an approximation based on local thermodynamic equilibrium is nonsense, or just a poor approximation, so that 'classical non-equilibrium thermodynamics' as proposed in the article is nonsense or such a poor approximation as to be practically worthless. The other is whether the idea of local thermodynamic equilibrium can be used to describe the procedure of cutting a rod, connecting two different temperatured heat baths, into segments, and bringing each segment to equilibrium at the appropriate temperature, and then putting the segments together in the original configuration and letting the re-composed rod settle to a smooth state? Can this kind of procedure be usefully extended into more complicated processes than mere heat conduction in a rod? Why?


 * It will take me time to get copies of your books, Thermodynamics of Irreversible Processes, McMillan, 1979, and A New Perspective on Thermodynamics, Springer, 2009. And more time to read them. I have plenty more questions, but cannot do everything at once.Chjoaygame (talk) 12:53, 9 March 2011 (UTC)

Dear Chjoaygame

The division of a body into disjoint, unevenly heated cells goes back to Thomson's 1852 paper. The gist of the paper can be found in Tait's book, Sketch of Thermodynamics, 1868. Thomson considers each cell equipped with an ideal engine so that when all the cells are put into thermal contact they will be able to do maximum work. In an unlimited amount of time, the final state of thermal equilibrium is reached where the temperature is the geometric mean of the initial temperatures. This is the lowest possible temperature, and consequently maximum work is done. If there are only two cells, the final temperature is (T_1T_2)^{1/2}. If I divide this by the higher temperature, say T_1, I get (T_2/T_1)^{1/2}. The efficiency, 1-(T_2/T_1)^{1/2}, just happens to be that of an endoreversible engine, which is claimed occurs in finite time. But, the same efficiency Thomson got in an unlimited amount of time, necessary to reach a final state of thermal equilibrium. Hence, it can't be gotten in a finite time and this throws out finite time thermodynamics: equal efficiencies but one needs and infinitely long time to reach thermal equilibrium while the other doesn't! The fact that the heat reservoir is not at the same temperature as the working substance creates irreversible processes (heat transport), and decreases the amount of work that can be done. For local equilibrium to exist and still have a macroscopic heat gradient, what would prevent the cells from equalizing their temperature differences? Is this the "smooth state" you refer to? Of course, I can imagine an idealized state of local equilibrium, but to what purpose? The entropy would be the same function of the extensive variables as in equilibrium so I would have no knowledge other than what I know at equilibrium. As I said, Prigogine used local equilibrium to be able to introduce the rate equations into the time derivative of his excess entropy. Any criterion of stability that can be obtained from this has nothing to do with the stability conditions given by the excess entropy itself. Hence, it cannot be a candidate for a Lyapounov function which says that sufficient stability exists if there is a function of definite sign throughout a finite region, and whose time derivative, evaluated along a trajectory of the motion, is of the opposite sign. If it could be a candidate for a Lyapounov function it would destroy its uniqueness, and the excess entropy applies to infinitesimal deviations from a stationary state while a Lyapounov function applies to stability in the large. The assumption of local equilibrium is counter productive because it decouples the function from its time derivative: the sign of the excess entropy is determined thermodynamically, while its time derivative, kinetically. — Preceding unsigned comment added by Bernhlav (talk • contribs) 13:50, 9 March 2011 (UTC)


 * Dear Bernhlav, Thank you for this reply. By the way, you can sign your posts by making four tilde marks in a row.


 * As I read your reply, it argues that the 'classical irreversible thermodynamics' (CIT) approach cannot be exactly right. I accept this, and I think everyone does.


 * The reason for my questions is to do with the general strategy of the Wikipedia article. At present the strategy is to accept the 'classical irreversible thermodynamics' method as an approximation of limited applicability, and to say that other methods exist but are not considered in the article. The reason for not considering them in the article is that they call for a more advanced understanding than the article can support. There is no suggestion that they are faulty; it is just that the article has limited scope. This strategy rests on the idea that there are problems which can be dealt with near enough by the classical approach, and its defect is its restricted range of applicability. According to Lebon Jou Casas-Vázquez 2008 on page 37: "this theory has been very useful in dealing with a wide variety of practical problems."


 * Your reply above is directed to the question of whether CIT is suitable for finding stability and extremal principles. This is an important question, but is a specialized question and is not the questions that I am at this stage of our discussion asking.


 * The possibility of stability and extremal principles is important and needs to be addressed, and probably much of what is said about it in the present article is flawed or perhaps simply wrong; revision is needed. But that should wait till the question is dealt with, of the usefulness of an introduction in terms of CIT. And still other questions remain. The general strategy of the article should be settled before making detailed revisions of special parts of the article.Chjoaygame (talk) 23:03, 9 March 2011 (UTC)

Dear Chjoaygame, I couldn't agree more. What does four tilde in a row do? Don't forget I am a newcomer, and have never contributed to Wikipedia. — Preceding unsigned comment added by Bernhlav (talk • contribs) 10:22, 10 March 2011 (UTC)


 * Dear Bernhlav, Thank you for this. Four tilde marks in a row generates your signature in the post. You can preview its effects by using the  key, and delete it if you don't like it. It forestalls the bot that otherwise generates an 'unsigned comment' entry.


 * I am asking you how far you think we should consider de-emphasizing the method of 'classical irreversible thermodynamics' (CIT) and its key notion of local thermodynamic equilibrium (LTE)? Are you considering abandonment of the strategy of basing the article on CIT and LTE as introductory methods, with only brief indications of other methods? If so, do you have another strategy that you think should be used? Is it too early to answer these questions?Chjoaygame (talk) 11:44, 10 March 2011 (UTC)


 * I will be occupied with other business for the next three days, and not able to read this page over that time.Chjoaygame (talk) 00:13, 11 March 2011 (UTC)

working over the page
Dear Chjoaygame

Hope you can read this page now. To answer your question, I would start with the historical background, and then proceed to compare the different "schools", much as I have done in TIP,1978: Onsager relations, their limitations and derivation from the principle of microscopic reversibility. Variational principles: Principle of least dissipation of energy via the constrained Rayleigh-Onsager dissipation function (not minimum entropy production which is a linear function of the fluxes). All this is in Onsager 1931. Then the microscopic justification via the Onsager-Machlup formulation for Gaussian processes in their 1953 articles. Callen and Greene fluctuation-dissipation function, Nyquist theorem and analysis of Gaussian processes. Afterwards a comparison of the rational thermodynamic formulation, generalized thermodynamics (local equilibrium), and extended thermodynamic (introduction of) inertial terms that appear in the second of the OM papers of 1953), nonlinear irreversible thermodynamics. Irreversible thermodynamic approach to stability. New advances can then be critically assest. What do you think? Bernhlav (talk) 13:49, 16 March 2011 (UTC)


 * Dear Bernhlav, thank you for this. Yes, I am back to this page now.


 * I find your approach sound but I think not altogether how the Wikipedia does things for this kind of article. The Wikipedia tends to have a way of doing things. Some parts of your approach would more likely go into a historical section of this article or into a separate article on the history. The present article needs much rewriting, but I think the shape should probably kept as it is, at least to some extent. At my end, my copy of TIP 1978 is still in the mail. I am reading some other related material, partly enlightened by the thought of your valuable critical input.


 * If you have time, could we go through the article as it stands and consider how to improve it?


 * The lead section is perhaps already a bit long, and should not be made longer.


 * The first paragraph is intended to announce the main direction of the article. Would you have time to comment on it? It reads: Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods; the fundamental difficulty for macroscopic thermodynamics is in defining entropy for systems not in thermodynamic equilibrium.


 * One thought that occurs to me is that perhaps the article should be not about non-equilibrium thermodynamics but about irreversible thermodynamics. There is a procedure for making such a name-change. On balance I am inclined to think that the present name, non-equilibrium thermodynamics, should be kept, but still I raise the question.


 * Perhaps the statement "the fundamental difficulty for macroscopic thermodynamics is in defining entropy for systems not in thermodynamic equilibrium" is wrong or misleading or otherwise inappropriate. I now think that perhaps the fundamental difficulty is in defining suitable variables of state, not in defining entropy? Perhaps you have some comments?


 * It may be enough for the new lead to end with this paragraph, and put the rest of the present lead, rewritten, into a new section called Introduction or Overview or somesuch. Later sections of the article will likely need more radical re-writing, or perhaps just deletion, when we get to them.Chjoaygame (talk) 11:03, 17 March 2011 (UTC)

Dear Chjoaygame:

I'm afraid I'm not familiar with Wikipedia and how it is organized.

Let me comment on some of the above. The statement that "most systems in nature are not in thermodynamic equilibrium because they are not in stationary states" is inaccurate. A stationary state is by definition a nonequilibrium state characterized by a constant flow that is maintained by a finite thermodynamic force. When the latter vanishes one has thermodynamic equilibrium. In chemical systems it is the law of mass action that determines the equilibrium state, or at the microscopic level, the principle of microscopic reversibility. The rate of transition from one state to another must be equal at equilibrium. I can also have a stationary state where the transition from A to B is equal to B to C is equal to C to A. An example is the famous Lotka-Volterra system.


 * The statement that "fundamental difficulty in defining entropy for systems not in thermodynamic equilibrium" is also not quite true. We know many of the properties of entropy; the first and foremost is that it is a concave function of its extensive variables. It can be both subadditive or superadditive. Entropies are determined by their probability distributions. In "Statistical Physics: A Probabilistic Approach" (Wiley, 1991) I reverse this and show that the entropy is the potential in the Gaussian law of error for which the average and most probable value coincide. This works for entropies which have logarithmic forms. It will not work for Bose-Einstein and Fermi-Dirac entropies which are proportional to the non-conserved particle number. In fact, Planck's discovery of his law of black-body radiation can be looked as a search for a logarithmic form of the entropy that would be valid for intervals of the frequency between dw and w+dw. The entropy turns out to be the logarithm of the negative binomial coefficient which is the Boltzmann entropy. Expressing the distribution in terms of the entropy as a function of the average value, or the thermodynamic entropy, and the entropy as a function of the fluctuating value, or the kinetic entropy, completes Boltzmann's principle by giving a normalized probability and as Planck referred to a "thermodynamic" probability which is a very large number. The corresponding entropy of the FD statistics is the logarithm of the binomial coefficient. In the limit where probability of success tends to zero while the number of trials increases without limit such that their product is constant, both distributions merge into the Poisson distribution where the entropy is the Gibbs entropy. This is Wien limit of bb radiation.


 * In addition there are the well-known entropies of information theory: the Hartley entropy corresponds to the Boltzmann entropy and the Shannon entropy to the Gibbs entropy. The gamut between them is bridged by the Renyi entropy, which is not really an entropy because it depends upon a parameter, and hence is different for systems with different parameters. Even though such systems may have the same number of degrees of freedom they are incomparable. Entropy must be comparable for different systems with the same number of degrees of freedom. Another "entropy" is the Havrda-Chavat entropy, which has recently become known as the Tsallis entropy, again is not an entropy because it depends on a parameter. The interest in it is that it is nonextensive, hence the "new" branch of nonextensive thermodynamics. The distinction between information theoretic entropies and thermodynamic entropies is that the former depend upon a set of probabilities while the latter on a set of extensive thermodynamic variables. Then there are entropy reductions that related to extreme value distributions which show the opposite behavior of tending to cluster about the most probable value as the sample size increases without limit [see for example "Thermodynamics of Extremes" (Horwood, Chichester, 1995)]. These, too, characterize nonequilibrum phenomena, among which are earthquakes, thermogravity, material brittleness, cracking and fracture, etc.

There is also the statistical foundations of nonequilibrium thermodynamics, if you take de Groot & Mazur as authorative. They have chapters on statistical foundations and fluctuation dissipation theorem.[see also "Nonequilibrium Statistical Thermodynamics" (Wiley, Chichester, 1985)]. Related to this is nonequilibrium work from equilibrium measurements, or the so-called Jarzynski equality) which I see the article already has a reference as the thermodynamics of small systems.

Since Wikipedia is so vast and so too nonequilibrium, or irreversible, thermodynamics, perhaps it is worth checking how many of these topics are covered in other articles and how the present article can then be linked to them without duplication. If you would like, I can do this as a preliminary step. Bernhlav (talk) 17:27, 17 March 2011 (UTC)


 * Dear Bernhlav, thank you for this. It is good to make a critical scrutiny of the page as you are doing.


 * I have tightened the grammar of the sentence which you find inaccurate. The old structure was of a principal clause with a subordinate compound adverbial clause of reason, but now I have made it a principal clause with a compound principal clause in illative coordination. The meaning is unchanged but the grammar is more text-book strict now.


 * I will now, with respect, defend the new sentence:"Most systems found in nature are not in thermodynamic equilibrium; for they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems."


 * The main statement is that "Most systems found in nature are not in thermodynamic equilibrium." The coordinated clauses give logical grounds for that. I am at present supposing that you agree with that main statement. If not, then the following reasons are premature and perhaps irrelevant.


 * The logical grounds offered are "they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems." These grounds argue as follows.
 * (1) If a system is not in a stationary state, then it cannot be in thermodynamic equilibrium. This reason regards thermodynamic equilibrium as a trivial stationary state. As I understand thermodynamic equilibrium, it excludes non-zero flow. Your definition requires that a stationary state include a non-zero flow; that means that, by definition, the trivial "stationary state" that is assumed by the present statement to be thermodynamic equilibrium is, by your definition, not counted as a genuine stationary state. It is indeed a trivial question as which definition should be used here. Since your definition uses the idea of a thermodynamic force, I would say that it is not an ordinary language definition but is a technical definition or term of art; this weakens its claim to a place in the lead, which is for newcomers. On the reading that a "stationary state" can include zero-flow states, the present wording seems safe to me. Your technical definition is valid as a technical definition, but is, I would say, somewhat arbitrary in its exclusion of the trivial "stationary state" of zero flow; and if it is to be used, it needs to be explicitly stated, and the lead is not the place for that.


 * You write: "I can also have a stationary state where the transition from A to B is equal to B to C is equal to C to A." This is so, but it says nothing about systems not in a stationary state; and therefore it does not impugn the presently stated logical ground.


 * (2) If a system is continuously and discontinuously subject to flux of matter and energy to and from other systems, then it does not have zero flow. But zero flow is a part of the definition of thermodynamic equilibrium as I understand it. Therefore a system continuously and discontinuously subject to flux of matter and energy to and from other systems is not in thermodynamic equilibrium.


 * For these reasons, I think the present wording is accurate. End of defence.


 * You write: "The rate of transition from one state to another must be equal at equilibrium." As I read this, you are using the word state to refer to the state of a microscopic constituent considered as able to exhibit several states and to pass between them? Or somesuch. This article is about thermodynamics, and the word state for that purpose usually refers to the whole macroscopic system, not to a microscopic component.


 * Please note how I have changed the typography to make your paragraphs fit on the monitor screen. Copying from above:"The statement that 'fundamental difficulty in defining entropy for systems not in thermodynamic equilibrium' is also not quite true. We know many of the properties of entropy; the first and foremost is that it is a concave function of its extensive variables. It can be both subadditive or superadditive. Entropies are determined by their probability distributions. In 'Statistical Physics: A Probabilistic Approach' (Wiley, 1991) I reverse this and show that the entropy is the potential in the Gaussian law of error for which the average and most probable value coincide. This works for entropies which have logarithmic forms. It will not work for Bose-Einstein and Fermi-Dirac entropies which are proportional to the non-conserved particle number. In fact, Planck's discovery of his law of black-body radiation can be looked as a search for a logarithmic form of the entropy that would be valid for intervals of the frequency between dw and w+dw. The entropy turns out to be the logarithm of the negative binomial coefficient which is the Boltzmann entropy. Expressing the distribution in terms of the entropy as a function of the average value, or the thermodynamic entropy, and the entropy as a function of the fluctuating value, or the kinetic entropy, completes Boltzmann's principle by giving a normalized probability and as Planck referred to a 'thermodynamic' probability which is a very large number. The corresponding entropy of the FD statistics is the logarithm of the binomial coefficient. In the limit where probability of success tends to zero while the number of trials increases without limit such that their product is constant, both distributions merge into the Poisson distribution where the entropy is the Gibbs entropy. This is Wien limit of bb radiation."


 * The immediate aim here is to state very briefly what is the main obstacle that stands in the way of equilibrium thermodynamics on a path to non-equilibrium thermodynamics. Can you offer a one-sentence indicator of that main obstacle?


 * Copying from above:"In addition there are the well-known entropies of information theory: the Hartley entropy corresponds to the Boltzmann entropy and the Shannon entropy to the Gibbs entropy. The gamut between them is bridged by the Renyi entropy, which is not really an entropy because it depends upon a parameter, and hence is different for systems with different parameters. Even though such systems may have the same number of degrees of freedom they are incomparable. Entropy must be comparable for different systems with the same number of degrees of freedom. Another 'entropy' is the Havrda-Chavat entropy, which has recently become known as the Tsallis entropy, again is not an entropy because it depends on a parameter. The interest in it is that it is nonextensive, hence the 'new' branch of nonextensive thermodynamics. The distinction between information theoretic entropies and thermodynamic entropies is that the former depend upon a set of probabilities while the latter on a set of extensive thermodynamic variables. Then there are entropy reductions that related to extreme value distributions which show the opposite behavior of tending to cluster about the most probable value as the sample size increases without limit [see for example 'Thermodynamics of Extremes' (Horwood, Chichester, 1995)]. These, too, characterize nonequilibrum phenomena, among which are earthquakes, thermogravity, material brittleness, cracking and fracture, etc."


 * Again, the immediate aim here is to state very briefly what is the main obstacle that stands in the way of equilibrium thermodynamics on a path to non-equilibrium thermodynamics. Can you offer a one-sentence indicator of that main obstacle?


 * Thank you for your care in this.Chjoaygame (talk) 06:52, 18 March 2011 (UTC)

Dear Chjoaygame,

Thank you for your clarification. The sentence:

Most systems found in nature are not in thermodynamic equilibrium; for they are not in stationary states, and are continuously and discontinuously subject to flux of matter and energy to and from other systems.

leads me to that that a stationary state is an equilibrium state. I distinguish stationary states from thermodynamic equilibrium as the former have constant fluxes while the latter has zero flux. So much is flowing into the system as it flows out of the system. So I can be in a stationary state and still not be in equilibrium, where, as you point out, has zero flow. Perhaps the following

Most systems found in nature are not in thermodynamic equilibrium; for they are temporally evolving as the result of gradients that create fluxes. Systems in which the fluxes are constant are called stationary states because they are time independent. It is only when the system is isolated that the fluxes vanish and thermodynamic equilibrium can be established. However, we have no way of knowing how long this may take since the system has been isolated from its environment, and also from the ability to make measurements on it. The concept of time does not enter into equilibrium thermodynamics in contrast to nonequilibrium thermodynamics.

The "A", "B" and "C" above can be chemical reactants, populations, etc. Equilibrium is then identified with the Guldberg-Waage law of mass action: the rate of reaction in the forward direction must be equal to that in the reverse direction at chemical equilibrium. This is also the principle of microscopic reversibility at equilibrium.

I think the main obstacle that stands in the "way of equilibrium thermodynamics on a path to nonequilibrium thermodynamics" is certainly the introduction of time into a theory that, by its very nature, precludes it.

Bernhlav (talk) 16:21, 18 March 2011 (UTC)


 * Dear Bernhlav, thank you for this. I have made an edit to remove the word stationary, and replace it with more ordinary language.


 * As for the obstacle, it is important that you have focused on definite time as the thing that distinguishes equilibrium from non-equilibrium thermodynamics. Can you offer a one-sentence ordinary-language indicator of the main reason why this is an obstacle?Chjoaygame (talk) 06:15, 19 March 2011 (UTC)

Dear Chjoaygame,

Thank you for your message. I have read the modified sentences, and my only query is what does "triggered" mean? As far as the obstacle of entropy is concerned [Grandy citation], I believe there are more than enough entropies around. According to an article of Peter Landsberg there are "Entropies Galore!" Consulting Landau and Lifshitz Sec. 54 of Statistical Physics, they define nonequilibrium entropies for the Fermi-Dirac and Bose-Einstein distributions quite easily. They follow the Callen and Greene principle which says that the fluctuating (nonequilibrium) entropy must have the same form as the equilibrium entropy if there are not to be two equilibrium thermodynamics: one microcanonical and the other canonical [cf. "Statistical Physics: A Probabilitistic Approach" (Wiley, 1991) Sec. 3.7 and reference notes]. So it's not the entropy which is the problem but how it acquires a time dependency through the fluctuating variables which the nonequilibrium entropy is a function of.

Also the reference to "Classical Non-equilibrium Thermodynamics" is the title of Chapter 2 of "Thermodynamics of Irreversible Processes" (Macmillan, 1978), which predates the 1993 reference you give.

The one sentence could be:

Whereas non-equilibrium processes evolve over time, the concept of time is completely foreign to equilibrium thermodynamics so that its introduction constitutes a major obstacle to generalizing equilibrium to non-equilibrium thermodynamics. Bernhlav (talk) 14:03, 19 March 2011 (UTC)


 * Dear Bernhlav, thank you for this.


 * I think 'triggered' is near enough ordinary language to express that a system in metastable equilibrium is not absolutely stable.


 * Right now we are still working just on the lead paragraph. We can work on the subsequent paragraphs over time; perhaps they may be moved into a new section. My copy of TIP 1978 is still in the snail mail. The Wikipedia seems to have no rule about how many relevant references may be given, nor about precedence.


 * My question is why is it a difficulty? Mere foreignness I think is not a sufficient answer. The fact that there are many proposed entropies is likely evidence that there is difficulty in selecting the right one. "The problem [is] how it acquires a time dependency" is perhaps a suitable pointer, but perhaps this is not the main difficulty? A definition of entropy for statistical thermodynamics is not the focus here. The focus here is on the macroscopic phenomenological approach. Chjoaygame (talk) 02:56, 20 March 2011 (UTC)

Dear Chjoaygame, Entropy has a unique role in that it has one foot in the macroscopic world and the other in the microscopic world. This is due to the second law: the entropy must be a concave function of all its variables. Planck, in his derivation of his spectral law for black-body radiation, confused concavity with its ability to increase in time. There is nothing in thermodynamics that would attribute a time dependency to the entropy. To get around this Caratheodory compared two states of equilibrium: a more and a less constrained state of equilibrium to show that entropy has the tendency to increase. It is greater in the less constrained state than in the more constrained state. The logarithmic form of the entropy makes it a potential for Gauss's error law; thus, there is an intimate relationship between its phenomenological and probabilistic roles. But for degenerate gases, the entropy is proportional to the unconserved particle number, and thus loses its logarithmic form. This is also true in relativistic thermodynamics where the entropy and particle number are relativistic invariants. For, if not, there would be a way of distinguishing relative motion from a state of rest as one being less ordered. So entropy always carries with it its probabilistic connotations. Moreover, Onsager had to avail himself of the principle of microscopic reversibility in order to prove his reciprocal relations. So any time we have derive general nonequilibrium principles we are obliged to consider fluctuations. The questioning of the word "trigger" was that stability hasn't been defined let alone metastability. It has always been my belief to give credit where credit is due.Bernhlav (talk) 09:31, 20 March 2011 (UTC)


 * Dear Bernhlav, thank you for this. Since you discuss entropy here I infer that you think it an important thing, in the present context, of my question about why the definite time aspect of non-equilibrium thermodynamics is a difficulty not present in equilibrium thermodynamics. Another candidate reason that strikes me is that, though one can do non-equilibrium thermodynamics for cyclic processes that don't explicitly consider the inner workings of a system but simply consider the time course of the exchanges between system and reservoirs, nevertheless, in much non-equilibrium thermodynamics, spatial inhomogeneity and new intensive variables that describe finite memory of materials are important, but do not matter for equilibrium thermodynamics. Perhaps we can leave this question and think about it for a while, and move on to the next section of the article.


 * My copy of A New Perspective on Thermodynamics arrived today and I have begun reading it.Chjoaygame (talk) 11:15, 21 March 2011 (UTC)

new section Overview
I am thinking of ending the lead section with the first paragraph as above, and starting a new section called Overview with the next paragraphs in the present lead section. Let us think about this new section, which can be re-written. The more detailed sections of the article I think are much in need of radical re-writing also, of course.Chjoaygame (talk) 11:15, 21 March 2011 (UTC)

Dear Chjoaygame,

Below is the next section on basics. My comments are in the square brackets.

There are many examples of stationary non-equilibrium systems, some very simple, like a system confined between two thermostats at different temperatures or the ordinary Couette flow, a fluid enclosed between two flat walls moving in opposite directions and defining non-equilibrium conditions at the walls. Laser action is also a non-equilibrium process, but it depends on departure from local thermodynamic equilibrium and is thus beyond the scope of classical irreversible thermodynamics; here a strong temperature difference is maintained between two molecular degrees of freedom (with molecular laser, vibrational and rotational molecular motion), the requirement for two component 'temperatures' in the one small region of space, precluding local thermodynamic equilibrium, which demands that only one temperature be needed. Damping of acoustical perturbations or shock waves are non-stationary non-equilibrium processes. Driven complex fluids, turbulent systems and glasses are other examples of non-equilibrium systems. [This paragraph has nothing to do with basics and is very confusing to the reader wanting to know what non-equilibrium thermodynamics is all about.]

The mechanics of macroscopic systems depends on a number of extensive quantities. It should be stressed that all systems are permanently interacting with their surroundings, thereby causing unavoidable fluctuations of extensive quantities.[The word fluctuation is wrong.] Equilibrium conditions of thermodynamic systems are related to the maximum property of the entropy. [Maximum with respect to what?] If the only extensive quantity that is allowed to fluctuate [vary!] is the internal energy, all the other ones being kept strictly constant, the temperature of the system is measurable and meaningful. The system's properties are then most conveniently described using the thermodynamic potential Helmholtz free energy (A = U - TS), a Legendre transformation of the energy. [Why? The definition of temperature is given below so that it is the entropy and not the Helmholtz free energy that defines it.] If, next to fluctuations of the energy, the macroscopic dimensions (volume) of the system are left fluctuating, we use the Gibbs free energy (G = U + PV - TS), where the system's properties are determined both by the temperature and by the pressure. Non-equilibrium systems are much more complex and they may undergo fluctuations of more extensive quantities.[This has nothing to do with non-equilibrium systems. You are defining intensive variables just as they are in equilibrium.] The boundary conditions impose on them particular intensive variables, like temperature gradients or distorted collective motions (shear motions, vortices, etc), often called thermodynamic forces. [No mention has been made of boundary conditions and are not relevant to what is being discussed.] If free energies are very useful in equilibrium thermodynamics, it must be stressed that there is no general law defining stationary non-equilibrium properties of the energy as is the second law of thermodynamics for the entropy in equilibrium thermodynamics. [I don't understand this sentence at all. Is it saying that the second law is only valid in equilibrium? Stationary non-equilibrium properties have not been defined.] That is why in such cases a more generalized Legendre transformation should be considered. This is the extended Massieu potential.[This is wrong. Legendre transform of the energy and Massieu transform for the entropy. Nothing to do with being more general.] By definition, the entropy (S) is a function of the collection of extensive quantities Ei. Each extensive quantity has a conjugate intensive variable Ii (a restricted definition of intensive variable is used here by comparison to the definition given in this link) so that:[So it is the inverse temperature that is the conjugate intensive variable? You will run into trouble when you come to P/T, the ratio of the pressure to temperature.]


 * $$ I_i = \partial{S}/\partial{E_i}.$$

We then define the extended Massieu function as follows:


 * $$\ k_b M = S - \sum_i( I_i E_i),$$

where $$\ k_b$$ is Boltzmann's constant, whence [What is Boltzmann's constant doing in a macroscopic formulation??]


 * $$\ k_b \, dM = \sum_i (E_i \, dI_i).$$

The independent variables are the intensities.[This is identically zero because of the Gibbs-Duhem equation. You can't have a thermodynamic potential which is a function only of intensive variables because you must know how big the system is, i.e., the volume, or how many particles it contains, i.e. the particle number.]

Intensities are global [local!] values, valid for the system as a whole. When boundaries impose to the system different local conditions, (e.g. temperature differences), there are intensive variables representing the average value and others representing gradients or higher moments. The latter are the thermodynamic forces driving fluxes of extensive properties through the system.[Where do boundaries come in? who defined them? Never heard of temperature as an average value. Where is the zero law of thermodynamics? The average temperature would be the final temperature at which the system arrives at!]

It may be shown that the Legendre transformation changes the maximum condition of the entropy (valid at equilibrium) in a minimum condition of the extended Massieu function for stationary states, no matter whether at equilibrium or not [Absolutely not. The Legendre transform applies to the energy, not entropy, and certainly doesn't convert maxima into minima.]

As you can see where it is not wrong, it is extremely confused, and will certainly confuse a reader who wants to know what the "basics" are. I have also read the article on entropy. That article has entropy "accumulating" in a Carnot cycle! Even though there is consensus, it is wrong. Bernhlav (talk) 12:18, 21 March 2011 (UTC)


 * Dear Bernhlav, thank you for this. I agree that the section you have commented on is unsatisfactory. I have not actually examined it closely, and I have not thought about how it should be revised. That is a task yet to be done.


 * Before working on that, I would like to make the new Overview section something along the lines of a re-written and revised version of the last four paragraphs of the present lead. The four paragraphs I mean are"Overview""The most widely understood approach to non-equilibrium thermodynamics can (Jou, Casas-Vázquez, Lebon (1993) ) be called classical irreversible thermodynamics. This approach demands spatial and temporal continuity of locally defined intensive variables such as temperature and internal energy density, which requires what is known as local thermodynamic equilibrium     (see also Keizer (1987) ). These are very stringent demands. This present article is focused on the restricted subject of classical irreversible thermodynamics.""Other concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Section II of Rayleigh (1873) ), and of time rate of entropy production (Onsager 1931), and dissipative structure.""Non-equilibrium thermodynamics is most successful in the study of steady states, where there are nonzero flows and entropy production, but no time variation, and of systems with dissipative structure . Such steady states and dissipative structures can sometimes be understood in terms of extremal principles in non-equilibrium thermodynamics.""There are other approaches to non-equilibrium thermodynamics, for example extended irreversible thermodynamics, but they are hardly touched on in the present article."


 * These four paragraphs need to be thoroughly re-considered, re-constructed, and re-written, but not made much longer.Chjoaygame (talk) 16:19, 21 March 2011 (UTC)

Dear Chjoaygame,

Perhaps something along theses lines?

The cornerstone of non-equilibrium thermodynamics is the linear, or classical, region where the phenomenological relations relating forces and fluxes are linear, and the integrability condition for the entropy production is ensured by the Onsager relations of the cross phenomenological coefficients.

Classical non-equilibrium thermodynamics can be characterized by the constrained variational principle of least dissipation of energy. The extremum condition yields the phenomenological relations, while the second variation of the Rayleigh-Onsager dissipation function is related to stability criteria which ensure that it is a minimum.

The same characterization of stationary states that are maintained by finite values of the thermodynamic forces requires some assumption, as local stable equilibrium, in order to eliminate the first order term in the expansion of the entropy production, which is a bilinear form of forces and fluxes, to second order. That is, the same quadratic form of the entropy production is used to characterize stationary states as if they were the state of equilibrium with the difference that there are now finite steady fluxes. Bernhlav (talk) 17:58, 21 March 2011 (UTC)


 * Dear Bernhlav, thank you for this. I think it is far too detailed and technical for this Overview section, but may well belong deeper in the article. Needed here are just indications or names of some of the main lines of thought that the article will follow, not actually following them right here. I take it from what you write here that you think that classical non-equilbrium thermodynamics is a suitable subject to be included in the article, and indeed that it should be expounded to some degree. Not being an expert, I do not know if there is a difference between local thermodynamic equilibrium and local stable equilibrium? Should mention be made here of other approaches, including extended irreversible thermodynamics, and theories with internal variables, and others?
 * What changes are needed in this paragraph:"The most widely understood approach to non-equilibrium thermodynamics can (Jou, Casas-Vázquez, Lebon (1993) ) be called classical irreversible thermodynamics. This approach demands spatial and temporal continuity of locally defined intensive variables such as temperature and internal energy density, which requires what is known as local thermodynamic equilibrium     (see also Keizer (1987) ). These are very stringent demands. This present article is focused on the restricted subject of classical irreversible thermodynamics."
 * What changes are needed in this paragraph:"Other concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Section II of Rayleigh (1873) ), and of time rate of entropy production (Onsager 1931), and dissipative structure."
 * What changes are needed in this paragraph:"Non-equilibrium thermodynamics is most successful in the study of steady states, where there are nonzero flows and entropy production, but no time variation, and of systems with dissipative structure."
 * What changes are needed in this paragraph:"Such steady states and dissipative structures can sometimes be understood in terms of extremal principles in non-equilibrium thermodynamics.""There are other approaches to non-equilibrium thermodynamics, for example extended irreversible thermodynamics, but they are hardly touched on in the present article."
 * Enough for now.Chjoaygame (talk) 12:00, 22 March 2011 (UTC)

Dear Chjoaygame,

A system is cut up into small cells, each of which is still considered to be macroscopic in size. Each cell has a slightly different value of an intensive variable. Seen from the outside it appears as a gradient. Each cell is said to be in local stable equilibrium, for if it were not stable it would not be in equilibrium and system would break up. The cells are described by the same thermodynamic functions as if it were in equilibrium with the same thermodynamic stability criteria as equilibrium. The assumption of local stable equilibrium is NOT the same as classical non-equilibrium thermodynamics. In particular you cannot sum all the cells to get a criterion for instability.

What is the time rate of dissipation of energy? and the time rate of entropy production? Being an over view these terms have not been defined. Rather you should stick to general variational principles which are local ones, i.e., point-wise.

Irreversible thermodynamics studies the time evolution of systems either displaced from equilibrium, where classical non-equilibrium thermodynamics applies, or to stationary states, where classical non-equilibrium thermodynamics (CNET) may not apply. The latter needs to take into account finite, constant thermodynamic forces and in any Taylor expansion of the forces and fluxes there will be linear terms in these forces.

Extended irreversible thermodynamics takes into consideration inertia: whereas CNET has a strict relationship between fluxes and forces, extended irreversible thermodynamics takes into account accelerative terms which have not been, as yet, damped out.

I will be out of town until Friday and unable to read this page.

Bernhlav (talk) 13:53, 22 March 2011 (UTC)

Dear Bernhlav, my copy of TIP has arrived, and now I can read it.Chjoaygame (talk) 02:17, 23 March 2011 (UTC) Now I am reading it and find it has valuable answers to questions which have been puzzling me for a long time, not answered in other books that I have read. It will take some time for me to understand it thoroughly. The ideas in it are rather sophisiticated and I have not seen them discussed elsewhere, but now I will be on the lookout.Chjoaygame (talk) 06:43, 23 March 2011 (UTC)

Abiogenesis
It would be good to see general and mathematical formalized materials on Abiogenesis Topics, derivable from subjects covered by those like Alexander Oparin, Miller Urey, and Joan Oro(sp?). The topic of Combinatorial Chemistry in homogeneous fluid environments, under cyclical concentration, electrical, thermal, and optical loads, like early earth oceans, under daily solar cycles, tides, and weather, is of critical importance, to understanding the origins of life in Abiogenesis Systems Methods. With a chemical soup rich with carbon related compounds in solutions, as the early earth ocean were, with all of the biomass stored in the oceans as non-living biomolecules, would produce numerous sub-networks of reactions within the larger frame of Brute Force Combinatorial Chemistry. It would be self organizing, producing reaction networks in the daytime, converting photon energy in energy storing molecules, and producing reaction networks in the nighttime, converting energy storing molecules into other molecules. Both forming a basis for proto-photosynthesis and metabolism. Likewise, in the greater superstucture of Brute Force Combinatorial Chemistry, the sub-networks of reactions in this proto-metabolism, would statistically favor durable, reactive, synergistic molecule network systems, in this Molecular Darwinism. The synergism aspect would be key, in the sense that the metabolic reaction sub-network molecules, that can reactively work with the background chemical soup of complex, yet otherwise dead end reaction products, would utilize this diverse main backround chemical soup as a molecular feeding ground, in their other two sub-network attributes of being both durable and reactive. The overall feedback properties of durable, reactive, synergy molecular sub-systems, would form the basis of life, in the necessary environment of exactly such a non-equilibrium thermodynamic system. Even Jupiter shows how non-equilibrium systems with extreme vorticity, and thermal cycles between interior and space, and weak solar loading, can produce a complex chemical atmospheric system, that is not anywhere near perfectly mixed as entropy might indicate, after four billion years of mixing. LoneRubberDragon-SET-236-765-732-171-160-170-744-543-253-750-714-909-VEL 76.166.233.62 (talk) 10:24, 4 August 2011 (UTC)


 * Perhaps a new main article would be the place for this kind of work. The bitter truth is that non-equilibrium thermodynamics would, in hope, like to have something useful to say about abiogenesis, but, in fact, is so poorly developed that it cannot even have much useful to say even about the general organization of the weather. True, Prigogine was a fine student of thermodynamics, but that does not make all his work truly a part of thermodynamics. To have a section about abiogenesis in the article on non-equilibrium thermodynamics would be in a sense pretentious, pretending that non-equilibrium thermodynamics is more advanced than it really is. One fundamental difficulty is that in abiogenesis, the distinction between work and heat is not sharp enough to be useful. Thermodynamics requires a sharp and clear distinction between work and heat. That distinction is not enough to organize the thinking processes in the study of abiogenesis, which therefore is in a sense a new subject in its own right. Statistical mechanics is more flexible than non-equilibrium thermodynamics and is perhaps more suited for the study of abiogenesis.Chjoaygame (talk) 20:44, 4 August 2011 (UTC)


 * The most disturbing thing is, perhaps, that all of humanity, in the very domain of study under such political rancor, religious associations, and physical and medical applications, of abiogenesis Non-Equilibrium Thermodynamics and Chemistry, with traces in Oparin 1920's, Miller Urey 1950's, and Joan Oro in the 1960's and 1970's, have all shown little result in analyzing the results of these non-equilibrium systems. It is as if the world loves mediocrity and hiding knowledge, with intentionally placed blind spots in thinking over many decades, of happy stupid children of humanity.  There IS more than work and heat.  There is photochemistry, did you forget?  Photons striking silver based molecules.  Photons striking silicon mineral surfaces in fluids.  The distinction between what some think is a response, and what is ueful knowledge, is the difference between flash and fizzle, of not so free speech in america and the world.  Pretensious is veils of division, written inj political spin statements, and little tiny minds acting like children under the law that makes all thermodynamics, the dynamics of death choice.  Oh well, have it your own little retarded world's way.  We could live in the 11th century like Islam Dictates, as another mere pretensious false infidel god who botched the universe up, if you believe that sort of rubbish. 76.166.233.62 (talk) 00:33, 5 August 2011 (UTC)

undid apparent self-promotion
The edits that I just undid seem to be self-promotion. They have two signatures, one just an address, the other a named editor. Unless there is some evidence that these were not self-promotion, they are not admissible edits.Chjoaygame (talk) 02:22, 11 May 2013 (UTC)

Reintroducing "Swensonism"
I was surprised to see no reference to Swenson on this page and just read this talk page, and wow. Pseudo-science it is not. The theory has recently gained some traction so I thought I would present some evidence here.

See DARPA's Physical Intelligence project: http://www.darpa.mil/Our_Work/DSO/Programs/Physical_Intelligence.aspx The most prominent supporters of "Swensonism" are a group at the University of Connecticut. (Yes, Swenson has some loose affiliation there but he was not involved in any of what I'm about to post). The UConn group was on DARPA's Physical Intelligence project for a time. You can see a figure from his paper under the second "Project Image". Receiving a grant from DARPA should be sufficient notability, I think, to warrant at least a small section.

Last year, the journal Ecological Psychology published two special issues on Physical Intelligence: http://www.tandfonline.com/toc/heco20/24/1 http://www.tandfonline.com/toc/heco20/24/3

Yes, this is the journal Swenson's original paper was published in (though he published in other places as well), and it is the journal the group at UConn is most associated with. However it is not affiliated with either Swenson or CESPA (the research center at UConn). It is a well-respected journal internationally, perhaps niche but not fringe. In these special issues, there are articles by psychologists, physicists, chemists, and philosophers, some well-known within their fields, clarifying and expanding Swenson's theory.

The work has many citations. One notable citation is Lynn Margulis's book What is Life? http://books.google.com/books?hl=en&lr=&id=VwsRNzrcCf4C&oi=fnd&pg=PR7&ots=5HzJJ1WvH3&sig=290OXKogoOYa8g6scy_tk1F9bz4#v=onepage&q=swenson&f=false — Preceding unsigned comment added by 75.69.168.45 (talk) 14:23, 16 May 2013 (UTC)


 * I for one will consistently oppose a re-introduction of Swensonism to this article. The name itself gives a hint as to its nature: ad hominem. All the remarks in the foregoing post advocating Swensonism are purely ad hominem. There is no trace of scientific argument in them. If perhaps Swensonism is important then perhaps it needs a Wikipedia article of its own. One has only to read Swenson's work to find out that it has practically no substantial content of scientific non-equilibrium thermodynamics. It is informed by specious, scientifically inappropriate teleology, that makes it pseudo-science, not fitting here, but perhaps fitting somewhere else.Chjoaygame (talk) 20:25, 16 May 2013 (UTC)

My remarks had no scientific arguments because it was solely a notability argument. I understand if you don't find any merit in Swenson's approach, and I'm not going to convince you as this is not my area of expertise. But I believe notability and not scientific merit is what makes a topic suitable for inclusion in an article, is it not? In any case, what deserves a mention is not Swenson's work specifically, but the work inspired by his dubbed "Physical Intelligence". (and by the way, I only used the term "Swensonism" because I had seen that in this or another talk page. I've not seen that anywhere else, especially not from its advocates). Maybe PI deserves its own page, but even if so it should be mentioned or at least linked here, probably in the 'Applications' section.

I have personally discussed PI with Dilip Kondepudi, who contributed to one of the EP issues I mentioned above. He recently was part of a symposium at a Psychology conference introducing non-equilibrium thermodynamics and Physical Intelligence to a psychological audience. He doesn't share the confidence of his collaborators (e.g. Swenson's original coauthor Michael Turvey) as to the proposed Law of Maximum Entropy Production but that clearly doesn't take away from his enthusiasm as to the prospect of understanding the physical basis of intelligence (in the most general sense of the word) from non-equilibrium thermodynamics. In other words, there is room for nuanced opinion here, no need to go full-blown "anything associated with Swenson is pseudoscience". The best compromise may be to consider PI not as contributing to non-equilibrium thermodynamics itself but as work inspired by it, and intimately connected to it. In that case what you would say as to a stand-alone article on Physical Intelligence, with a few sentences under "Applciations" here? 71.235.146.28 (talk) 20:48, 30 July 2013 (UTC)


 * With respect, Swensonism is pseudo-science. There is no room for "nuanced opinion" about that. I don't see it as "inspired" by non-equilibrium thermodynamics; I would see it as trying to exploit the name of non-equilibrium thermodynamics as a specious garment for pseudo-science. A simply scientific article such as the present one should not give any support to it, not even mention or refer to it. Swensonism is not relevant to non-equilibrium thermodynamics, and is therefore not notable for it.


 * Many of us, including me, think that intelligence is, in principle, probably open to explanation by physical science, but we in the physical sciences don't see Swenson as coming even remotely near doing it; at present, physical science is so far from it that talk of it is almost automatically pseudo-science. I have no opinion about a stand-alone article on Physical Intelligence, whatever that might intend, but I oppose any mention of it here, or any suggestion in Wikipedia that it currently has a proper scientific basis. I think it is a pseudo-scientific oxymoron.


 * In a word, no.Chjoaygame (talk) 22:13, 30 July 2013 (UTC)

It doesn't seem to me that you're replying "with respect." In fact, quite the opposite. You claim to speak for "we in the physical sciences" in dismissing Physical Intelligence despite the fact that there are scientists like Kondepudi -- whose seminal textbook on thermodynamics you recommended on this very page -- working on it! Skepticism is one thing, but your hostility is completely unwarranted, and your implication that your view is shared by the field in general is flat-out wrong. 71.235.146.28 (talk) 04:14, 31 July 2013 (UTC)


 * I am sorry that it doesn't seem to you that I am "replying with respect, indeed quite the opposite". I don't see how I can easily persuade you that I am treating you with respect. The difficulties in connecting between the physical science viewpoint and the whole of human experience viewpoint are very great. Physical science proceeds by deliberately narrowing its viewpoint, more or less in a Cartesian way, separating the res extensa from the res cogitans, and simply using the res cogitans as an explanatory apparatus, seeking to explore and explain the res extensa, but not considering the res cogitans as an ontological part of the res extensa. The res extensa is constituted so as to be ontologically devoid of elements of res cogitans. The huge problem for physical science is to proceed within its own framework to eventually discover a structure that matches that of the res cogitans, but is still ontologically apart from it. This is already getting into a mighty philosophical complexity, and not suitable for this talk page or for an article on non-equilibrium thermodynamics. Non-equilibrium thermodynamics has huge problems even properly defining entropy for a full non-equilibrium problem. Trying to use it for studying intelligence is like asking a very premature baby to fly a space-ship with general relativistic controls. Way out of our league. I don't want to make a struggle of this. I do respect your interest, but I can't just say "Oh, ok, it's just a point-of-view problem." No, it's a matter of different ball-parks. I have spent plenty of time on this question, and am not just making this up off the top of my head now, but I don't think it's appropriate to try to go into it here.Chjoaygame (talk) 16:55, 31 July 2013 (UTC)

it would be nice to have the reasons for this edit
Anonymous Editor 208.99.241.102 has strongly weakened the expression of the page about work by Tschoegl, with no covering explanation for his edit. It would be of interest to know why his modification is so strong. It is most comfortable for other editors when editors sign themselves in with their own account names. It is not clear from the edit and its cover note whether Editor 208.99.241.102 has himself actually read the work by Tschoegl, or whether he is just expressing his feeling that the support given in the page for Tschoegl's work seemed excessive and lacking neutrality or secondary support. Perhaps Editor 208.99.241.102 may be right, but it would be nice to have some reason from him for his edit. This talk page would be the place for that reason now.Chjoaygame (talk) 10:25, 15 March 2014 (UTC)

undid a valuable edit that needs work before it can be accepted
I undid the edits because more work is needed on their content and setting out, and because the English is faulty.

It is evident that the material offered is valuable and I hope that Editor Annakremen will do what is needed to make it acceptable, and not be discouraged by this initial rejection.

The change of section heading as an afterthought indicates a lack of planning of the work. The Prigogine proposition is of narrow scope, and this should be reflected in the structure of the article. The new material is of far wider scope, and this should be indicated by its being presented in a format that makes this clear. That it claims to cover financial markets raises much doubt about its logic. This is because financial markets do not have Hamiltonian dynamics. I am not sure, but I think some of the logic of other parts of the edits is faulty.

The new material is mostly, I think, new research that has not been presented in critical secondary sources. It is, however, presented as established knowledge. Its relation to other relevant work is not discussed. It is not clear whether the edit may be written by a related party, which would raise the question of conflict of interest. The English is flawed throughout.

Broadly speaking, the edits give an impression of soap-boxing. This could be remedied by citing critical review of their content.

I am glad that we have you here, Editor Annakremen. I hope you will persist. Your approach needs to be more critically neutral or disinterested, and your setting out of the material should be better organized. Secondary source criticism is needed. You need some way to get the English right.Chjoaygame (talk) 17:13, 16 November 2014 (UTC)

but not impossibility
I removed the added parenthesis "(but not impossibility)" partly because it was unsourced and partly because the best sources say its message is wrong.

I do not know exactly what the anonymous IP editor has in mind here, but I can say that the best sources say that entropy is not defined for non-equilibrium states. Many physicists would dearly love to see entropy defined for non-equilibrium states, but that is wishful thinking.Chjoaygame (talk) 01:56, 30 March 2015 (UTC)

External links modified
Hello fellow Wikipedians, I have just added archive links to 1 one external link on Non-equilibrium thermodynamics. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes: When you have finished reviewing my changes, please set the checked parameter below to true to let others know.
 * Added archive https://web.archive.org/20140520040325/http://onlinelibrary.wiley.com/doi/10.1002/qj.49710142906/abstract to http://onlinelibrary.wiley.com/doi/10.1002/qj.49710142906/abstract

Cheers. —cyberbot II  Talk to my owner :Online 09:58, 19 October 2015 (UTC)

Reasons for rewrite
A banner was added last month saying that a complete rewrite may be required. Has there been an ongoing discussion about why a rewrite is necessary and how it should proceed? I myself have not contributed to this article in the past, but am interested in doing so in the future. MaxwellMolecule (talk) 16:45, 17 January 2019 (UTC)


 * It is good to see an interest in this article. A minor point: it is customary here to add new material below old material, not above it. I trust you will be happy that I have shifted it accordingly.Chjoaygame (talk) 09:02, 18 January 2019 (UTC)


 * No problem. I trust most people will be patient enough to scroll to the bottom :-) MaxwellMolecule (talk) 13:20, 18 January 2019 (UTC)
 * I'm removing the sentence in the beginning that says: "Non-equilibrium thermodynamics is a work in progress, not an established edifice." It's not clear to me what that means, there is no reference for it, and it seems like a POV or OR statement. I assume it means something like "Non-equilibrium thermodynamics is a relatively new field filled with controversy and different opinions" but since I don't know if that is true (or even what the editor who wrote that had in mind) I'm just removing the statement. So far though, I don't see much justification for the tag. The tag itself is incredibly vague. Doesn't meet Wikipedia standards in what way? Not enough references? Not encyclopedic? I think it is irresponsible to put a tag like that on an article without providing some specific justification and suggestions for change in the Talk page which I don't see. Unless I see other problems in the article (or someone else can provide better justifications or suggestions for changes) I'm going to remove that tag. --MadScientistX11 (talk) 20:08, 11 July 2020 (UTC)
 * After reading the introduction, I'm leaving the tag. The introduction is hard to understand for someone who isn't a specialist in the field. I'm pretty science literate (but just an amateur in physics) and have been studying other article in Wikipedia on Thermodynamics and entropy. Most of them are well written but at least the introduction here was very hard to follow and jumped into spewing jargon rather than giving a clear, high level overview of what the topic is about that non experts can understand. I think I get the gist which is that the concept of non-equilibrium is to some extent relative since almost all systems are (depending on how carefully one measures) not at equilibrium but I'm not sure that's what it means and if that is what it means it could be said more clearly. --MadScientistX11 (talk) 20:20, 11 July 2020 (UTC)


 * As remarked below, the topic of non-equilibrium thermodynamics has a lot of literature, but much of it, even in widely cited textbooks, is more wishful thinking than Wikipedia-reliably sourced and established science. The topic attracts attention because it might seem useful. Indeed, as in the foregoing comment, "the concept of non-equilibrium is to some extent relative". A carefully chosen system can be near enough to thermodynamic equilibrium to give sense to the prime concepts of thermodynamics such as entropy and temperature.


 * But the vaster extents of the universe have always been and still are very far from thermodynamic equilibrium. For example, it would be hard to think of a physical process or situation further from thermodynamic equilibrium than the celebrated 'big bang'. Yet one sometimes reads, even from one top physicist, that the universe must have started in a state of low entropy in order for its entropy to have been increasing throughout its duration. The essence of entropy is that it describes the extreme symmetry of thermodynamic equilibrium; it makes no sense to speak of the entropy of the universe in its earliest existence. It is desirable to give the reader something of perspective, perhaps such as in Grandy's Entropy and the Time Evolution of Macroscopic Systems (2008). The now removed sentence was so intended.


 * To extend thermodynamics to substantially non-equilibrium situations or processes, that is to say, to processes of substantial change, it is necessary to extend the concept of entropy to two-or-more-time domains. So far as I know, no one knows how to measure such an extended concept.Chjoaygame (talk) 21:53, 11 July 2020 (UTC)

New diagram, request to change caption
Editor Nzjacobmartin has kindly created and supplied a new diagram, derived from a published journal article. The terminology of the journal article, written from its own particular and special point of view, and used in the diagram, does not agree with that of this Wikipedia article, which takes a more general point of view.

The diagram's concept of "energy" can be precisely defined only for a scenario near enough to thermodynamic equilibrium to qualify as local thermodynamic equilibrium. In this case, entropy will also be defined near enough, so that it will make sense to regard the scenario as described by thermodynamics. The diagram shows states separated by large energy barriers. This signifies that fluctuations are small enough to allow a steady state, and that the cardinal energy state variable is well defined. If the scenario were far from equilibrium, so that local thermodynamic equilibrium did not prevail, then entropy and the cardinal energy state variable would not be defined, and so the terms of the diagram would be undefined.

For the purposes of this article, the caption of Nzjacobmartin's diagram should be written from the more general point of view of this article. For the purposes of this article, I would like to ask Nzjacobmartin to very kindly please change the diagram's words "Far from equilibrium" to 'Local thermodynamic equilibrium with steady state energy flow'.Chjoaygame (talk) 21:11, 7 May 2019 (UTC)


 * I agree. Local thermodynamic equilibrium is necessary for the diagram to make sense. MaxwellMolecule (talk) 22:59, 7 May 2019 (UTC)


 * Thank you for your responses.


 * Yes, Editor Nzjacobmartin, you are right that I was too restrictive in focusing on the steady state scenario. As you say, time variation is also admissible. Still, local thermodynamic equilibrium is necessary for the figure to belong in an article on thermodynamics. Then my little commentary with its heading needs to be changed. Anticipating this, I have changed it.


 * Yes, Editor MaxwellMolecule, I agree that the condition of local thermodynamic equilibrium is appropriate here.


 * Accordingly, I ask that the caption of the figure be changed so as to express that local thermodynamic equilibrium prevails in the scenario of the figure.Chjoaygame (talk) 04:44, 8 May 2019 (UTC)


 * Does Editor Nzjacobmartin's new figure have a well defined abscissa? What does it express? Without an answer to these questions, the meaning of the figure is hardly defined.Chjoaygame (talk) 16:32, 9 May 2019 (UTC)


 * I have now more carefully read the paper by Mattia et al. cited for the new diagram. I have also read more closely the relevant books cited by Editor Bernhlav. I now point out that the paper by Mattia et al. does not offer reasons why its far-from-equilibrium régime should have a defined entropy, nor does it actually say that it has a defined entropy. Nor does the article give an adequate definition of its "energy" ordinate, consonant with its lack of defined entropy. This means that it does not fall within the scope of Wikipedia-reliably sourced (WP:RS) non-equilibrium thermodynamics. Consequently I would like to thank Editor Nzjacobmartin for his careful good-faith contribution, but I regret to say that I think his diagram is unsuitable for the present article. In general, in this kind of Wikipedia article, a single journal article does not constitute a Wikipedia-reliable source; the present situation fits this general rule. Reliable textbooks are more likely to constitute reliable sources. The topic of non-equilibrium thermodynamics has a lot of literature, but much of it, even in widely cited textbooks, is more wishful thinking than Wikipedia-reliably sourced and established science.Chjoaygame (talk) 02:18, 10 May 2019 (UTC)

reasons for undo
I have undone the edits of 14 May 2019 that referred to self-organising criticality, that cited Per Bak's book How Nature Works: the science of self-organized criticality. Thank you, Editor SpinodalCactus, for your interest in this article, and your edits.

For four decades I have been interested in self-organized criticality. I have undone the edits for several reasons. Per Bak's own text, that is the cited reference of the undone edits, so far as I can tell, does not actually use the word 'thermodynamics'; the word appears in the title of one article that he cites. Bak's book is not much about thermodynamics. It is a rather enthusiastic monograph, even adventurous or speculative, or even lacking in the kind of scholarship one looks for in a Wikipedia-reliable source, though I found it interesting to read. Self-organizing critical states, though dynamic and non-equilibrium, do not seem to be good examples of scenarios so far from thermodynamic equilibrium that one cannot imagine that some future development of non-equilibrium thermodynamics may be able to deal with them. Scenarios that are really very far from equilibrium include explosions. Perhaps one might say that the little and big disasters that mediate scenarios of self-organized criticality are such; perhaps, but that doesn't quite seem to amount to a convincing example of something that no future thermodynamic method might be able to deal with. I think that the reason why some scenarios might be for ever beyond the scope of thermodynamics is that they depend so much on the adventures of so many atoms that the number of degrees of freedom of the system would be so great that the term 'thermodynamics' would hardly apply. Self-organized criticality seems to have more structure than that, so that one can imagine a reasonably manageable number of degrees of freedom being enough.

If you want to put something in the article about the relevance of self-organized criticality for non-equilibrium thermodynamics, perhaps you may work out a satisfactory way of doing so. I don't think that Per Bak's book How Nature Works qualifies as a reliable source; it is too adventurous and speculative. I am inclined to think that it would be better to deal with self-organized criticality in its own article, which might perhaps mention thermodynamics.Chjoaygame (talk) 07:38, 14 May 2019 (UTC)


 * I cited Per Bak's book because it had some examples of systems where there is self-organized criticality, even with nonvariational mechanisms. I do understand that the citation is confusing since the origin on the impossibility of applying the non-equilibrium methods to systems emerges from this point (since the entropy production cannot be connected to any free energy or Gibbs entropy production relation). It can be discussed that since non-equilibrium thermodynamics is not a complete theory, there can be patches to this general problem, but the methods of the non-variational theory are outside of the original ideas of relating entropy production to conserved quantities.SpinodalCactus(talk 13:54,14 May 2019 (UTC)


 * Thank you your new edit, expressing a better reason, and for your valuable comment here.Chjoaygame (talk) 18:57, 14 May 2019 (UTC)

"Law of maximum entropy production" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Law of maximum entropy production and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 February 5 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Shhhnotsoloud (talk) 09:09, 5 February 2022 (UTC)