Statistical mechanical proof of the second law of thermodynamics based on volume entropy

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (1):181-194 (2008)
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Abstract

In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely mechanical way and suggests that the volume entropy might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of microscopic (quantum or classical) mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law. We discuss how this result relates to the Minimal Work Principle and improves over previous attempts. The natural evolution of entropy is towards larger values because the natural state of matter is at positive temperature. Actually the Law of Entropy Decrease holds in artificially prepared negative temperature systems.

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References found in this work

Bluff Your Way in the Second Law of Thermodynamics.Jos Uffink - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (3):305-394.
The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law.Harvey R. Brown & Jos Uffink - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):525-538.
The Principles of Statistical Mechanics.Richard C. Tolman - 1939 - Philosophy of Science 6 (3):381-381.
On the mechanical foundations of thermodynamics: The generalized Helmholtz theorem.Michele Campisi - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):275-290.

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