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On the Clausius inequality

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Summary

A condition equivalent to the existence of the absolute temperature scale satisfying the Clausius inequality is exhibited. The condition is close to the classical statements of the second law of thermodynamics due to Clausius and others. It is formulated as an assertion about cyclic processes of bodies whose totality is called a universe of bodies. The universe can contain general (local or not) bodies with memory but the validity of the result (i.e., the mentioned equivalence) requires that it must contain enough elastic bodies. With each universe of bodies one can associate a collection of Borel measures on the real line, and the restrictions imposed on the universe of bodies induce certain properties of this collection. Also the condition equivalent to the existence of the absolute temperature scale as well as the Clausius inequality can be stated completely in terms of the collection of measures. The proof of the main result is given in this more general setting without recourse to bodies.

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Authors and Affiliations

  1. Mathematical Institute, Czechoslovak Academy of Sciences, Žitná 25, 11567, Prague 1, Czechoslovakia

    M. Šilhavý

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  1. M. Šilhavý
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Communicated by J. Serrin

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Šilhavý, M. On the Clausius inequality. Arch. Rational Mech. Anal. 81, 221–243 (1983). https://doi.org/10.1007/BF00250801

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  • DOI: https://doi.org/10.1007/BF00250801

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