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This question came to my mind when I was reading the 8th chapter of "Heat and Thermodynamics, 7th edition, Zemansky-Dittman". The book somehow concludes that "Principle of increase of entropy" of the universe is a principle/postulate/axiom and the "Second law of thermodynamics" is just the result of this principle much like in a manner that we say "Principle of conservation of energy" of the universe is more fundamental than the "First law of thermodynamics".

Now this is my question:

Is "Principle of increase of entropy" more fundamental or "2nd law of Thermodynamics" is more fundamental? Which one?

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    $\begingroup$ Most of the time the "Principle of increase of entropy" and the second law would be treated as synonymous. How exactly are they being defined in this case? $\endgroup$ – By Symmetry Nov 23 '16 at 12:01
  • $\begingroup$ @BySymmetry In the book most of the times the 2nd law of TD is: "Thermal energy wouldn't transfer from Cold system to the Hot system spontaneously." But the principle mentioned is: "The overall entropy of an isolated system(or the universe) is perpetually increasing." $\endgroup$ – Hamed Begloo Nov 23 '16 at 12:07
  • $\begingroup$ @CountTo10 Of course the book says the Entropy of subsystems of the isolated system could decrease but in cost of increasing the rate of increase of entropy of surrounding systems but in overall the system's total entropy is increasing. $\endgroup$ – Hamed Begloo Nov 23 '16 at 12:20
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    $\begingroup$ Either can be derived from there other, they are equivalent axioms. On one hand, "increasing entropy" has the most clear statistical interpretation. One the other, the "Clausius statement" of the second law, is most apparent in day to day life. The choice is yours. $\endgroup$ – Reid Hayes Nov 23 '16 at 12:24
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    $\begingroup$ Couple of comments here. (1) I never really liked that line in Zemansky. (2) There is no such thing as a fundamentalnessometer; questions like "which of [A] or [B] is more fundamental?" are basically polls. In some cases there will be consensus and others not. In this case I favor the entropy concept because I find it cleaner, but I don't claim that is some kind of natural law. $\endgroup$ – dmckee Nov 23 '16 at 18:54
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Is "Principle of increase of entropy" more fundamental or "2nd law of Thermodynamics" is more fundamental? Which one?

It depends on how one defines "fundamental". Current day physics accepts that the underlying level of nature is quantum mechanical. That is the fundamental level. Classical mechanics emerges from the underlying quantum mechanical level. Statistical mechanics is an application of classical mechanics to small classically interacting particles. Thermodynamics can be proven to emerge from classical statistical mechanics, and not the other way. Thus one can say that the increase in entropy which is definable in statistical mechanics is more fundamental than the second law of thermodynamics.

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  • $\begingroup$ Thank you for your answer. Another question: As we know conservation laws arise from the symmetries existing in the universe, can we also conclude that non-conservation laws (like "Increase in entropy") arises from some asymmetries existing in the universe? $\endgroup$ – Hamed Begloo Nov 23 '16 at 15:30
  • $\begingroup$ I do not know the answer to this. At first glance "non conservation laws" would seem to be too many to classify easily $\endgroup$ – anna v Nov 23 '16 at 15:56
  • $\begingroup$ Another question: Are these laws still valid at quantum mechanical levels? Since we know mass-energy could be generated out of nothing(violation of conservation of energy) and causality would not exist and it means the arrow of time vanishes(violation of increase of entropy). $\endgroup$ – Hamed Begloo Nov 23 '16 at 16:03
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    $\begingroup$ non general relativity quantum mechanics has a defined entropy counting states. General relativity is another story at the moment, but there is no standard quantization theory (string theories are candidates). Once that is done I suspect entropy will again be defined $\endgroup$ – anna v Nov 23 '16 at 17:28
  • $\begingroup$ Thank you. If you don't mind I prefer the question to be remained open to see others' opinions as well. Best regards. $\endgroup$ – Hamed Begloo Nov 23 '16 at 19:17
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"the 8th chapter of "Heat and Thermodynamics, 7th edition, Zemansky-Dittman". The book somehow concludes that "Principle of increase of entropy" of the universe is a principle/postulate/axiom"

This is a lie. "Entropy always increases" is a THEOREM deduced by Clausius in 1865:

http://philsci-archive.pitt.edu/archive/00000313/ 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."

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  • $\begingroup$ It isn't a theorem. Clausius statement follows from the I and II principle of thermodynamics, which in turn follow from the entropy variational principle if used as starting point from the equations of motion of thermodynamics. $\endgroup$ – gented Nov 23 '16 at 15:28
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    $\begingroup$ Most non-trivial physical principle can be built (in an internally consistent and usable way) from multiple different sets of axiomatic statements. That a particular statement is a theorem in one such construct doesn't prevent it from being an axiom in another. Nor is the first formulation that comes up historically necessarily the best either for application or for pedagogical purposes. Noting what the historical first form was would be an interesting comment, but libelous statements are bad answers under any circumstance and frankly reflect much more badly on you than any one else. $\endgroup$ – dmckee Nov 23 '16 at 18:51
  • $\begingroup$ "That a particular statement is a theorem in one such construct doesn't prevent it from being an axiom in another." Justified logically, unjustified physically. For instance, you can declare the Lorentz transformation equations to be an axiom (postulate), and derive Einstein's 1905 two initial assumptions from it - they will be both "theorems" in this scenario. Some Einsteinians do teach something like that, and they are correct logically, but... $\endgroup$ – Pentcho Valev Nov 23 '16 at 20:32

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