Violations of the Second Law of Thermodynamics

Pentcho Valev

Nature: "Second law broken. Researchers have shown for the first time that, on the level of thousands of atoms and molecules, fleeting energy increases violate the second law of thermodynamics. [...] They found that over periods of time less than two seconds, variations in the random thermal motion of water molecules occasionally gave individual beads a kick. This increased the beads' kinetic energy by a small but significant amount, in apparent violation of the second law." http://www.nature.com/news/2002/020722/full/news020722-2.html

This was published in 2002 and immediately forgotten. In thermodynamics, crimestop is even stronger than in relativity:

George Orwell: "Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."

Still I am going to show in this thread that violations of the second law of thermodynamics are, actually, commonplace.

"However, in experiments in which a capacitor is submerged in a dielectric liquid [e.g. deionized water] the force per unit area exerted by one plate on another is observed to decrease. [...] This apparent paradox can be explained by taking into account the DIFFERENCE IN LIQUID PRESSURE in the field filled space between the plates and the field free region outside the capacitor." http://farside.ph.utexas.edu/teaching/jk1/lectures/node46.html

The submerged capacitor experiment is able to violate the second law of thermodynamics, and the DIFFERENCE IN LIQUID PRESSURE is essential. If a small hole is punched in one of the plates, the high interplate pressure will produce a permanent flow through the hole. This flow can be harnessed to do work, at the expense of ambient heat.

Water in an electric field automatically becomes a perpetual-motion machine of the second kind. Vigorous motion is generated that can do work (e.g. by rotating waterwheels) at the expense of ambient heat (there is no other source of usable energy):

Pentcho Valev

Countless materials reversibly contract and then swell as a chemical agent (e.g. hydrogen ions) is added to and then removed from the system:

These materials can obviously do work. Here are two illustrations of how, by adding and removing hydrogen ions (H+), one can cyclically extract work from pH-sensitive polymers:

Figure 4 here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1367611/pdf/biophysj00645-0017.pdf

Figure 16A here: https://pubs.acs.org/doi/pdf/10.1021/jp972167t.

Adding and removing H+, per se, consumes no work if done QUASISTATICALLY. This means that the work lost e.g. in adding is compensated by the work gained in removing, and the net work involved in adding and removing H+ is zero. So lifting a weight is the net work extracted from the cycle. The second law of thermodynamics is clearly violated.

billslugg

This concept is nothing new, only the demonstration of it is new. The Second Law of Thermodynamics is statistical, there can always be minute violations in very small collections of particles. There is no practical application of this. See Maxwell's Demon.
Here is a note from Nature Magazine twenty years ago:
"In 1878, the physicist James Clerk Maxwell wrote in a book review for Nature:
The truth of the second law is ... a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules... Hence the second law of thermodynamics is continually being violated, and that to a considerable extent, in any sufficiently small group of molecules belonging to a real body."
Second law broken | Nature

As to your second point in post #1:
There is no mention in the citation of a violation of the Second Law. This is your assumption. Work is done at the expense of heat. Entirely consistent with the Second Law

As to your third point in post #1:
The water bridge is maintained by the energy inputted by the electric field. The cited manuscript contains no mention of any violation of the Second Law. This is your assumption and is not supported by the facts.

As to your post #2, point #1:
From the article:
"chemical fuel is efficiently consumed to generate macroscopic motion"
No violation of any laws

As to your post #2, points #2 and #3:
Adding and removing hydrogen ions introduces energy into the system. You are ignoring the energy losses due to friction. No violation.

Pentcho Valev

I am not a fan of Daniel Sheehan but still I am going to refer to him as he belongs to the physics establishment and his words and writings may discourage energetic defenders of the second law of thermodynamics:

Daniel P. Sheehan | Beyond the Thermodynamic Limit

"In 2000, a simple, foundational thermodynamic paradox was proposed: a sealed blackbody cavity contains a diatomic gas and a radiometer whose apposing vane surfaces dissociate and recombine the gas to different degrees (A_2 ⇌ 2A). As a result of differing desorption rates for A and A_2 , there arise between the vane faces permanent pressure and temperature differences, either of which can be harnessed to perform work, in apparent conflict with the second law of thermodynamics. Here we report on the first experimental realization of this paradox, involving the dissociation of low-pressure hydrogen gas on high-temperature refractory metals (tungsten and rhenium) under blackbody cavity conditions. The results, corroborated by other laboratory studies and supported by theory, confirm the paradoxical temperature difference and point to physics beyond the traditional understanding of the second law." https://link.springer.com/article/10.1007/s10701-014-9781-5

"A simple device is introduced that utilizes the phenomenon of epicatalysis to establish a stationary temperature difference by which ambient environmental thermal energy might be converted into useful work. [...] Traditional catalysis is a central pivot around which much of the industrial and biological worlds turn. Positive catalysts satisfy three general principles. First, they increase reaction rates by providing lower activation energies for rate-limiting steps. Second, they are not consumed by their net reactions although they are intimately involved in them. Third, they do not alter final thermodynamic equilibria of their reactions. Epicatalysts bend this third principle in that they shift the final gas-phase equilibria of reactions." D. P. Sheehan, T. M. Welsh, Epicatalytic thermal diode: Harvesting ambient thermal energy, Sustainable Energy Technologies and Assessments, Volume 31, February 2019, Pages 355-368 https://www.sciencedirect.com/science/article/pii/S2213138818301838

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Pentcho Valev

An absurd corollary of the second law of thermodynamics is that catalysts don't shift the position of chemical equilibrium. In other words, any catalyst speeds up the forward and reverse reaction rates equally (by exactly the same factor):

"In the presence of a catalyst, BOTH THE FORWARD AND REVERSE REACTION RATES WILL SPEED UP EQUALLY, thereby allowing the system to reach equilibrium faster. However, it is very important to keep in mind that the addition of a catalyst has no effect whatsoever on the final equilibrium position of the reaction. It simply gets it there faster. [...] If the addition of catalysts could possibly alter the equilibrium state of the reaction, this would violate the second rule of thermodynamics..." https://courses.lumenlearning.com/introchem/chapter/the-effect-of-a-catalyst/

Scientists should have noticed the absurdity of this particular corollary of the second law of thermodynamics long ago, and applied reductio ad absurdum: Since the corollary is absurd, the underlying premise, the second law of thermodynamics, is false. Consider the dissociation-association reaction

A ⇌ B + C

which is in equilibrium. We add a catalyst and it starts splitting A - the rate constant of the forward (dissociation) reaction increases by a factor of, say, 745492. If the second law of thermodynamics is obeyed, the catalyst must increase the rate constant of the reverse (association) reaction by exactly the same factor, 745492. But this is insane! The reverse reaction is entirely different from the forward one: B and C must first get together, via diffusion, and only then can the catalyst join them to form A. Catalysts don't speed up diffusion!

That catalysts can shift chemical equilibrium, thereby violating the second law of thermodynamics, was my first heretical idea, about 30 years ago. Journals used to reject my submissions, as it were, before receiving them. Still the idea is correct:

View: https://youtu.be/WhnIhzTIzd8?t=1107

"As its name implies, epicatalysis is related to standard catalysis, but with a twist. Conventional (positive) catalysts satisfy the three criteria, specifically they: (i) speed up their chemical reactions by providing low activation energy routes between reactants and products; (ii) participate in, but are not consumed by, their chemical reactions; and (iii) do not alter the final equilibria of their reactions. Epicatalysts abide by conditions (i) and (ii), but they break (iii)." https://www.scientificexploration.org/docs/34/jse_34_3_Sheehan.pdf

Far from speeding up the forward and reverse reactions "equally", in this experiment

Yu Hang Li et al. Unidirectional suppression of hydrogen oxidation on oxidized platinum clusters https://www.nature.com/articles/ncomms3500

a catalyst speeds up only the forward reaction, 2H+ → H_2, and SUPPRESSES the reverse reaction, H_2 → 2H+ (violation of the second law of thermodynamics par excellence).

Pentcho Valev

The metastases of Einstein's 1905 constant-speed-of-light malignancy definitively killed physics, but this branch of science was already in agony in 1905, overwhelmed by the metastases of another malignancy: the second law of thermodynamics. An instructive review here: http://philsci-archive.pitt.edu/313/1/engtot.pdf

Clifford Truesdell, The Tragicomical History of Thermodynamics, 1822-1854, p. 6: "Finally, I confess to a heartfelt hope - very slender but tough - that even some thermodynamicists of the old tribe will study this book, master the contents, and so share in my discovery: Thermodynamics need never have been the DISMAL SWAMP OF OBSCURITY that from the first it was and that today in common instruction it is; in consequence, it need not so remain." [...] p. 333: "Clausius' verbal statement of the "Second Law" makes no sense, for "some other change connected therewith" introduces two new and unexplained concepts: "other change" and "connection" of changes. Neither of these finds any place in Clausius' formal structure. All that remains is a Mosaic prohibition. A century of philosophers and journalists have acclaimed this commandment; a century of mathematicians have shuddered and averted their eyes from the unclean." https://www.amazon.com/Tragicomical-Thermodynamics-1822-1854-Mathematics-Physical/dp/1461394465

Jos Uffink, Bluff your way in the Second Law of Thermodynamics: "I therefore argue for the view that THE SECOND LAW HAS NOTHING TO DO WITH THE ARROW OF TIME. [...] Before one can claim that acquaintance with the Second Law is as indispensable to a cultural education as Macbeth or Hamlet, it should obviously be clear what this law states. This question is surprisingly difficult. The Second Law made its appearance in physics around 1850, but a half century later it was already surrounded by so much confusion that the British Association for the Advancement of Science decided to appoint a special committee with the task of providing clarity about the meaning of this law. However, its final report (Bryan 1891) did not settle the issue. Half a century later, the physicist/philosopher Bridgman still complained that there are almost as many formulations of the second law as there have been discussions of it. And EVEN TODAY, THE SECOND LAW REMAINS SO OBSCURE that it continues to attract new efforts at clarification." http://philsci-archive.pitt.edu/313/1/engtot.pdf

Pentcho Valev

There is an oversimplified but unambiguous formulation of the second law of thermodynamics suggested by Sadi Carnot himself (see the quotation below). If heat is to be cyclically converted into work (that is, if a heat engine is to be operative), then

"a cold body is necessary".

In other words, heat cannot be cyclically converted into work (a heat engine will not be operative) unless some temperature gradient is present: a hot body, source of heat, and a cold body, receiver of heat, must be available. Only two-temperature heat engines are possible; isothermal (one-temperature) heat engines don't exist. This false claim is universally taught nowadays:

"A necessary component of a heat engine...is that two temperatures are involved" http://physics.bu.edu/~duffy/py105/Heatengines.html

The problem is that in 1824 Carnot deduced "a cold body is necessary" from a postulate that eventually turned out to be false:

Carnot's (false) postulate: Heat is an indestructible substance (caloric) that cannot be converted into work by the heat engine.

Unpublished notes written in the period 1824-1832 reveal that, after realizing that his postulate was false, Carnot found "a cold body is necessary" implausible:

Sadi Carnot, REFLECTIONS ON THE MOTIVE POWER OF HEAT, p. 225: "Heat is simply motive power, or rather motion which has changed form. It is a movement among the particles of bodies. Wherever there is destruction of motive power there is, at the same time, production of heat in quantity exactly proportional to the quantity of motive power destroyed. Reciprocally, wherever there is destruction of heat, there is production of motive power." p. 222: "Could a motion (that of radiating heat) produce matter (caloric)? No, undoubtedly; it can only produce a motion. Heat is then the result of a motion. Then it is plain that it could be produced by the consumption of motive power, and that it could produce this power. All the other phenomena - composition and decomposition of bodies, passage to the gaseous state, specific heat, equilibrium of heat, its more or less easy transmission, its constancy in experiments with the calorimeter - could be explained by this hypothesis. But it would be DIFFICULT TO EXPLAIN WHY, IN THE DEVELOPMENT OF MOTIVE POWER BY HEAT, A COLD BODY IS NECESSARY; why, in consuming the heat of a warm body, motion cannot be produced." http://www.nd.edu/~powers/ame.20231/carnot1897.pdf

Generally, a cold body is not necessary, which means that the second law of thermodynamics is false. The cold body is only TECHNOLOGICALLY necessary as it makes heat engines fast-working. Heat engines working under isothermal condition (in the absence of a cold body) are commonplace but are too slow and impuissant to be of any technological importance. Except, perhaps, for the case in which water is placed in an electric field. The non-conservative force (pressure) that emerges in the bulk of water produces vigorous flows able to convert ambient heat into work:

Wolfgang K. H. Panofsky, Melba Phillips, Classical Electricity and Magnetism, pp.115-116: "Thus the decrease in force that is experienced between two charges when they are immersed in a dielectric liquid can be understood only by considering the effect of the PRESSURE OF THE LIQUID ON THE CHARGES themselves." http://www.amazon.com/Classical-Ele...ond-Physics/dp/0486439240?tag=viglink21401-20

"However, in experiments in which a capacitor is submerged in a dielectric liquid the force per unit area exerted by one plate on another is observed to decrease... [...] This apparent paradox can be explained by taking into account the DIFFERENCE IN LIQUID PRESSURE in the field filled space between the plates and the field free region outside the capacitor." http://farside.ph.utexas.edu/teaching/jk1/lectures/node46.html

Tai Chow, Introduction to Electromagnetic Theory: A Modern Perspective, p. 267: "The strictly electric forces between charges on the conductors are not influenced by the presence of the dielectric medium. The medium is polarized, however, and the interaction of the electric field with the polarized medium results in an INCREASED FLUID PRESSURE ON THE CONDUCTORS that reduces the net forces acting on them." http://www.amazon.com/Introduction-To-Electromagnetic-Theory-Perspective/dp/0763738271

Pentcho Valev

Arthur Eddington: "The law that entropy always increases—the Second Law of Thermodynamics—holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." https://todayinsci.com/E/Eddington_Arthur/EddingtonArthur-Entropy-Quotations.htm

"Entropy was discovered when it was noticed to be a quantity that behaves as a function of state, as a consequence of the second law of thermodynamics." https://www.scientificlib.com/en/Physics/LX/Entropy.html

It was Clausius who "noticed" that. Here is the story:

If you define the entropy S as a quantity that obeys the equation dS=dQrev/T, you will find that, so defined, the entropy is a state function FOR AN IDEAL GAS. Clausius decided to prove that the entropy (so defined) is a state function for ANY system. He based his proof on the assumption that any cycle can be disintegrated into small Carnot cycles, and nowadays this proof remains the only justification of "Entropy is a state function":

"Carnot Cycles: S is a State Function. Any reversible cycle can be thought of as a collection of Carnot cycles - this approximation becomes exact as cycles become infinitesimal. Entropy change around an individual cycle is zero. Sum of entropy changes over all cycles is zero." http://mutuslab.cs.uwindsor.ca/schurko/introphyschem/lectures/240_l10.pdf

The assumption on which "Entropy is a state function" is based - that any cycle can be subdivided into small Carnot cycles - is obviously false. An isothermal cycle CANNOT be subdivided into small Carnot cycles. A cycle involving the action of conservative forces CANNOT be subdivided into small Carnot cycles.

Conclusion: The belief that the entropy is a state function is totally unjustified. Any time scientists use the term "entropy", they don't know what they are talking about. For that reason, the concept of entropy always wins:

Scientific American: "When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one knows what entropy really is, so in a debate you will always have the advantage." https://www.esalq.usp.br/lepse/imgs/conteudo_thumb/Energy-and-Information.pdf

Pentcho Valev

The Clausius statement of the second law of thermodynamics:

"Heat can never pass from a colder to a warmer body without some other change connected therewith, occurring at the same time."

This version of the second law of thermodynamics is very popular because, like "Entropy always increases", it makes no sense (scientists love nonsensical statements and never abandon them):

Clifford Truesdell, The Tragicomical History of Thermodynamics, 1822–1854, p. 333: "Clausius' verbal statement of the "Second Law" makes no sense, for "some other change connected therewith" introduces two new and unexplained concepts: "other change" and "connection" of changes. Neither of these finds any place in Clausius' formal structure. All that remains is a Mosaic prohibition. A century of philosophers and journalists have acclaimed this commandment; a century of mathematicians have shuddered and averted their eyes from the unclean." https://www.amazon.com/Tragicomical-Thermodynamics-1822-1854-Mathematics-Physical/dp/1461394465

Here is an oversimplified presentation of Clausius' 1850 argument:

Premise: Heat can never pass from a colder to a warmer body SPONTANEOUSLY.

Conclusion: Heat can never pass from a colder to a warmer body REVERSIBLY.

The premise is (trivially) true but the conclusion does not follow from it (the argument is invalid). This would have been easily noticed if Clausius had not fatally confused the issue: his 1850 formulation of the conclusion essentially coincided with the premise. That is, Clausius deduced, even though invalidly, the conclusion

"Heat can never pass from a colder to a warmer body REVERSIBLY",

but the terms he used in the formulation of the conclusion were misleading so nowadays the conclusion is known as

"Heat can never pass from a colder to a warmer body without some other change connected therewith, occurring at the same time",

a statement which coincides with the premise.

Here is Clausius' 1950 argument:

"Ueber die bewegende Kraft der Wärme", 1850, Rudolf Clausius: "Carnot assumed, as has already been mentioned, that the equivalent of the work done by heat is found in the mere transfer of heat from a hotter to a colder body, while the quantity of heat remains undiminished. The latter part of this assumption--namely, that the quantity of heat remains undiminished--contradicts our former principle, and must therefore be rejected... [...] It is this maximum of work which must be compared with the heat transferred. When this is done it appears that there is in fact ground for asserting, with Carnot, that it depends only on the quantity of the heat transferred and on the temperatures t and tau of the two bodies A and B, but not on the nature of the substance by means of which the work is done. [...] If we now suppose that there are two substances of which the one can produce more work than the other by the transfer of a given amount of heat, or, what comes to the same thing, needs to transfer less heat from A to B to produce a given quantity of work, we may use these two substances alternately by producing work with one of them in the above process. At the end of the operations both bodies are in their original condition; further, the work produced will have exactly counterbalanced the work done, and therefore, by our former principle, the quantity of heat can have neither increased nor diminished. THE ONLY CHANGE will occur in the distribution of the heat, since more heat will be transferred from B to A than from A to B, and so on the whole heat will be transferred from B to A. By repeating these two processes alternately it would be possible, WITHOUT ANY EXPENDITURE OF FORCE OR ANY OTHER CHANGE, to transfer as much heat as we please from a cold to a hot body, and this is not in accord with the other relations of heat, since it always shows a tendency to equalize temperature differences and therefore to pass from hotter to colder bodies." http://www.mdpi.org/lin/clausius/clausius.htm

It is easy to see that the two-substances process considered by Clausius presupposes the action of an OPERATOR; this operator constantly and unavoidably undergoes CHANGES, changes that are absent when heat spontaneously "shows a tendency to equalize temperature differences and therefore to pass from hotter to colder bodies". So the trivial fact that, in a spontaneous process, in the absence of an operator, heat always flows from hot to cold by no means implies that heat will flow from hot to cold in a non-spontaneous operator-driven process as the one discussed by Clausius.

Clausius' argument is not just invalid; Clausius additionally confused it so it became "not even wrong". Not-even-wrong wisdoms are impossible to eradicate. Like Clausius' 1865 argument concluding that "Entropy always increases", and like Einstein's 1905 argument leading to the breathtaking "travel into the future", Clausius' 1850 argument is a malignancy that permanently belongs to the spirit of the civilization. Malignancies affecting human mind and their metastases will destroy the civilization quicker than material catastrophes.

Dragrath

Ok you seem to be making a big deal about this but one thing that tends to get missed is that we now know that the second law of thermodynamics is a consequence of information theory that is to say it is the criteria needed to be able to in principal reconstruct the past state of a system.

Most of this stuff you have posted seems to be quite old well over a century well before the more formal and explicit formalism of information theory and fields which depend on its principals namely statistical mechanics and quantum mechanics. This context is important because it shows you clearly lack a real understanding of the subject as you are trying to apply historical work to a modern context without recognizing that such work must be viewed within its historical context.

Really if we want to talk about the laws of thermodynamics there are two different ways of framing it one is what today is most familiar is the statistical argument which largely arises from the probabilistic interpretations of quantum mechanics. However there is still the deterministic model as while it has largely fallen out of favor thanks to bell tests this may be quite premature since Bell's inequality only ruled out "local" hidden variable theories"

The key nuance here is that the definition of "local" in question depends on the context of information you consider meaning it treats objects and or as independent of each other. This in the statistical context means only the wave function associated with the current state is considered not the past state evolution of the system.

However if we look at the Einstein field equations themselves and account for that spacetime is expanding and that expansion scales locally based on the rate of time experienced in a given space then it means information needed to reconstruct those initial conditions can and will have propagated beyond the local horizon at a rate dependent on the past lightcone and thus the rate of expansion so long as the speed of information transfer is much less than the size of the universe.

Work by Matthew Kleban and Leonardo Senaore from 2016 moreover shows with a theorem they call the "no big crunch theorem" explicitly that in the large scale limit i.e. where the size of the universe approaches infinity that for any arbitrarily inhomogeneous and anisotropic unconstrained Einstein field equations shows that for any initially expanding universe the total volume of this universe in any time slice will only ever be able to grow since the criterion for the metric to be able to reach an inflection point where expansion can reverse is logically forbidden for all possible choices of initial conditions.

Moreover this is because the attraction of matter to over densities will always result in a greater number of under densities which will thus cause the off diagonal elements of the metric tensor to grow in magnitude without bounds causing the expansion of space to accelerate overall. This is because they show that the off diagonal elements of the metric so long as conditions aren't perfectly symmetric at all scales must be conserved that is to say the universe can't grow more symmetric with a forward time slice differential from any frame of reference a.k.a. arrow of time.

In the context of information theory where information is defined as that which is needed to reconstruct the state of the system we can see this is a natural consequence of the conservation of information interacting with the local variation in the rate of expansion and path dependence of geodesics through the metric in General relativity, (what is more commonly known as gravitational lensing). In this sense we can see the no big crunch theorem is equivalent to the second law of thermodynamics which in turn is the criterion that the metric must meet in order for it to remain internally self consistent avoiding logical paradoxes.

As a whole this results in a universe with nonlocal correlations to the total volume or entropy of space within any time slice frame of reference. This is consistent with Bell's inequality the very thing which supposedly eliminated determinism arising naturally from enforcing internal consistency to a deterministic set of differential equations

The context of this is that it suggests a more deterministic explanation for thermodynamics and entropy is still on the table with the added benefit that it also resolves the cosmological crises plaguing the field of cosmology by showing one of the core assumptions namely that the off diagonal elements of the metric tensor should go to zero at large distances is unilaterally false for all nontrivial metrics in the large scale limit size of universe is much larger than the speed of causality.

There is much more to say but this is already quite dense so I'll stop here. Hopefully it resolves some misconceptions.

billslugg

billslugg

Thank you for a clear explanation of the subject. Much of it is over my head but I will strive to understand it.

Pogo

Pentcho Valev

Thank you for a clear explanation of the subject. Much of it is over my head but I will strive to understand it.

This http://philsci-archive.pitt.edu/313/1/engtot.pdf helped me a lot. Uffink is not an explicit second law denier (if he was, he would not have become professor at the University of Minnesota) but his criticism goes so far that the reader unavoidably starts doubting the validity of the law.

billslugg

Sorry, if you can't explain it to me in clear language right here, like Dragath did, I am not interested. I am not going to do your work for you by going to "Bluff your way in the Second Law of Thermodynamics" by Jos Uffink, and wade through 44,552 words.

Dragrath and Pogo

Pentcho Valev

Arthur Eddington: "The law that entropy always increases—the Second Law of Thermodynamics—holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." https://todayinsci.com/E/Eddington_Arthur/EddingtonArthur-Entropy-Quotations.htm

The version of the second law of thermodynamics stated as "Entropy always increases" is in fact a theorem deduced by Clausius in 1865:

Jos Uffink, Bluff your Way in the Second Law of Thermodynamics, p. 37: "Hence we obtain: THE ENTROPY PRINCIPLE (Clausius' version) For every nicht umkehrbar [irreversible] process in an adiabatically isolated system which begins and ends in an equilibrium state, the entropy of the final state is greater than or equal to that of the initial state. For every umkehrbar [reversible] process in an adiabatical system, the entropy of the final state is equal to that of the initial state." http://philsci-archive.pitt.edu/313/1/engtot.pdf

Clausius' deduction was based on three postulates:

Postulate 1 (implicit): The entropy is a state function.

Postulate 2: Clausius' inequality (formula 10 on p. 33 in Uffink's paper) is correct.

Postulate 3: Any irreversible process can be closed by a reversible process to become a cycle.

All the three postulates remain totally unjustified even nowadays. Postulate 1 can easily be disproved by considering cycles (heat engines) converting heat into work in ISOTHERMAL conditions. Postulate 3 is almost obviously false:

Uffink, p.39: "A more important objection, it seems to me, is that Clausius bases his conclusion that the entropy increases in a nicht umkehrbar [irreversible] process on the assumption that such a process can be closed by an umkehrbar [reversible] process to become a cycle. This is essential for the definition of the entropy difference between the initial and final states. But the assumption is far from obvious for a system more complex than an ideal gas, or for states far from equilibrium, or for processes other than the simple exchange of heat and work. Thus, the generalisation to all transformations occurring in Nature is somewhat rash."

Note that, even if Clausius's theorem were correct (it is not), it only holds for "an adiabatically isolated system which begins and ends in an equilibrium state". This means that all applications of "Entropy always increases" to processes which do not begin and end in equilibrium would still be unjustified!

Pentcho Valev

Many years ago I discussed the second law of thermodynamics in a few articles. I don't like them now, but...history is history:

The Law of Self-Acting Machines and Irreversible Processes with Reversible Replicas https://web.archive.org/web/20041114195215/http://content.aip.org/APCPCS/v643/i1/430_1.html (paywall unfortunately)

Biased Thermal Motion and the Second Law of Thermodynamics https://www.gsjournal.net/Science-Journals/Research Papers/View/760

19th Century Thermodynamics: The Beginning of the End of Theoretical Science https://www.gsjournal.net/Science-Journals/Research Papers/View/762

Pentcho Valev

"...concentration difference is generated internally by a chemically-asymmetric membrane that drives anisotropic diffusion of electrolyte ions, rather than being provided by an external source." https://www.sciencedirect.com/science/article/pii/S2213138822002466#b0005

Violation of the second law of thermodynamics par excellence. To avoid trouble, the authors

1. don't mention the Maxwell's demon, even though the analogy is obvious.

2. discuss the violation of the second law of thermodynamics in an ambiguous way that would calm down fierce critics:

"This behavior is thermodynamically intriguing. The repeated reversion from
pH = 0.00 to pH = - 0.01 indicates a spontaneous sorting of hydrogen ions from a maximum entropy state – one in which [H+] is the same in both chambers – to a lower entropy state, one in which they are 2% different. On its face, this spontaneous reduction in entropy without work input seems at odds with traditional understandings of entropy and the second law [25] but, of course, there is actually no conflict when the entropy changes associated with the walls and membrane are combined with those of the solutions...The
pHs and the resultant electrical power appear to be derived from the thermal diffusion of hydrogen ions, hence from purely thermal energy. At first glance this seems at odds with the second law of thermodynamics; however, as specified by the cell half-reactions, the anode continuously grows (precipitating AgCl) at the expense of the cathode, which will eventually disappear and bring the AMCC to a halt. Further investigation of AMCC thermodynamics seems warranted."

M.Bqoor

This research paper includes evidence of a violation of the 2nd law of thermodynamics:
employing ratchet potential in a circular formation produces continuous disequilibrium in the thermodynamic system.

M.Bqoor

This research paper includes evidence of a violation of the 2nd law of thermodynamics:
employing ratchet potential in a circular formation produces continuous disequilibrium in the thermodynamic system.
Additional preprint of the subject above can be found at:

billslugg

Here is a detailed explanation from MIT. In short, the Brownian Ratchet simply converts one type of work into another:

"Why is a Brownian motor not a perpetuum mobile of the second kind?
As long as the ratchet potential is off the particle will move diffusively according to a (biased) random walk, leading to a variance in position of
and a mean position of
, where D = kT /
is the diffusion constant. When the ratchet potential is switched on, the particle gets trapped in one of the potential minima. If
for the variance holds, the particle on average gets trapped into the minimum left to the starting point. The maximum flux is obtained if the switching time
is large enough to assure that the particle can adjust in the trapping minimum ('adiabatic adjustment time') and also is small enough to fulfill the above requirement for the variance. One can say roughly that a net flux to the left always occurs, when thermal energy is significantly smaller than the potential maximum, the external force is chosen not too big and the driving frequency matches the adiabatic adjustment time needed for the particle to move into a potential minima.

Where does the energy come from leading to a drift against the external force? The energy does not come from the heat bath but from the ratchet potential when it is switched on. At that moment the potential energy of the particle will be suddenly increased. In the simulation this can be seen by a sudden increase of the energy bar. But most of the energy pushed into the system will be just dissipated into the heat bath due to the relaxation of the particle into a potential minima. Only a tiny portion will be used for doing work. Thus a Brownian motor does not violate any law of thermodynamics it only turns one type of work into another one. Nevertheless the fluctuating force due to the heat bath is essential for a Brownian motor.

For more details and possible applications in biology and chemistry read the following review article:
R.D. Astumian: Thermodynamics and Kinetics of a Brownian Motor, Science 276, p. 917-922 (1997)."

Atlan0001

Atlan0001

Something went wrong and I couldn't reply directly to the above. Doesn't matter, though.

I hardly understood a bit of your post, and still think I got a good gist from my own understanding of Chaos Theory and the Science of Complexity. Particularly, I think, my understanding of the "zoom universe," the zoom level function, detailed in Chaos Theory, and the build and collapse of complexity detailed in the Science of Complexity. You understand in your language, and I understand in mine, and I think sometimes that, ultimately, we aren't all that far apart on certain subjects regardless of mind bend to language understood and used.

I'm a "visual mathematician," not a mathematician as such more than the average, but complexity and chaos come easy for me, given my interest in the subject. And what I can see as simple is often too complicated and ponderous for some, like that formulaic math of yours and others is too much a math (word) salad for me . . . just too complicated and ponderous for me. As a youngster I did a lot of shortcutting formulas, got enough right answers -- being told I was "intuitive" -- to pass exams with an A or a B average and still ended up with C grades for never sticking to formulas or even wanting to understand the formulas . . . for my interests and purposes regarding the complexity and the chaos of things, being especially good with computers and information tech, processing, and communication before I retired and fell behind the rapid evolutions . . . to which, being retired, I've said, "So what?!"

Enough of that.

So, thumbs up for your delving into the second law.

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billslugg

Thank you for your kind words.

I just ignore the equations. If someone is not considerate enough to provide a listing of variables complete with name and units, I am not going to be considerate enough to try and decode them.

Atlan0001

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