Athel Cornish-Bowden against Rudolf Clausius

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Athel Cornish-Bowden https://en.wikipedia.org/wiki/Athel_Cornish-Bowden: "The concept of entropy was introduced to thermodynamics by Clausius, who deliberately chose an obscure term for it, wanting a word based on Greek roots that would sound similar to "energy". In this way he hoped to have a word that would mean the same to everyone regardless of their language, and, as Cooper [2] remarked, he succeeded in this way in finding a word that meant the same to everyone: NOTHING. From the beginning it proved a very difficult concept for other thermodynamicists, even including such accomplished mathematicians as Kelvin and Maxwell; Kelvin, indeed, despite his own major contributions to the subject, never appreciated the idea of entropy [3]. The difficulties that Clausius created have continued to the present day, with the result that a fundamental idea that is absolutely necessary for understanding the theory of chemical equilibria continues to give trouble, not only to students but also to scientists who need the concept for their work." https://www.beilstein-institut.de/download/712/cornishbowden_1.pdf

Athel Cornish-Bowden is correct. Any thermodynamicist would (reluctantly) agree that, if the entropy is not a state function, then it is nonsense (nothing). Is there any valid proof that the entropy is a state function? There is none. Here is an oversimplified history of the entropy concept:

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: https://socratic.org/questions/is-entropy-state-function-how-prove-it. Clausius decided to prove that the entropy (so defined) is a state function for ANY system. He based his argument on the false assumption that any cycle can be disintegrated into small Carnot cycles, and nowadays this remains the only "proof" that 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 statement "Any reversible cycle can be thought of as a collection of Carnot cycles" is a blatant lie. An isothermal cycle CANNOT be thought of as a collection of Carnot cycles, a cycle involving action of conservative forces CANNOT be thought of as a collection of Carnot cycles, etc. etc.

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:

"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, nobody knows what entropy really is, so in a debate you will always have the advantage." https://en.wikipedia.org/wiki/History_of_entropy

Professor Jos Uffink, University of Minnesota: "I therefore argue for the view that the second law has nothing to do with the arrow of time...This summary leads to the question whether it is fruitful to see irreversibility or time-asymmetry as the essence of the second law. Is it not more straightforward, in view of the unargued statements of Kelvin, the bold claims of Clausius and the strained attempts of Planck, to give up this idea? I believe that Ehrenfest-Afanassjewa was right in her verdict that the discussion about the arrow of time as expressed in the second law of the thermodynamics is actually a red herring." http://philsci-archive.pitt.edu/313/1/engtot.pdf
 
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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 extremely popular because, like "Entropy always increases", it makes no sense:

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

Post-truth scientists reduce the Clausius statement to

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

and leave it at that. Try to refute this, miserable critics, if you still exist!
 
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The version of the second law of thermodynamics known as "Entropy always increases" is in fact a theorem deduced by Clausius in 1865 from a few false assumptions. One of them is that any irreversible process can be closed by a reversible process to become a cycle:

Jos Uffink, professor at the University of Minnesota, 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." http://philsci-archive.pitt.edu/313/

"The assumption is far from obvious" is a misleading euphemism. "Irreversible process closed by a reversible process to become a cycle" is oxymoron. So even if the entropy were a state function (it is not), "Entropy always increases" would remain nonsense.