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Mechanical Proof of the Second Law of Thermodynamics Based on Volume Entropy

Campisi, Michele (2007) Mechanical Proof of the Second Law of Thermodynamics Based on Volume Entropy. [Preprint]

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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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    Item Type: Preprint
    Keywords: quantum adiabatic theorem; minus first law; negative temperature; minimal work; Helmholtz theorem; arrow of time
    Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
    Depositing User: Michele Campisi
    Date Deposited: 26 Apr 2007
    Last Modified: 07 Oct 2010 11:15
    Item ID: 3316
    URI: http://philsci-archive.pitt.edu/id/eprint/3316

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