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Entropy 2018, 20(5), 328; https://doi.org/10.3390/e20050328

The Gibbs Paradox: Lessons from Thermodynamics

Department of Philosophy and Religious Studies, Utrecht University, Janskerkhof 13, 3512 BL Utrecht, The Netherlands
Received: 31 March 2018 / Revised: 15 April 2018 / Accepted: 27 April 2018 / Published: 30 April 2018
(This article belongs to the Special Issue Gibbs Paradox 2018)
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Abstract

The Gibbs paradox in statistical mechanics is often taken to indicate that already in the classical domain particles should be treated as fundamentally indistinguishable. This paper shows, on the contrary, how one can recover the thermodynamical account of the entropy of mixing, while treating states that only differ by permutations of similar particles as distinct. By reference to the orthodox theory of thermodynamics, it is argued that entropy differences are only meaningful if they are related to reversible processes connecting the initial and final state. For mixing processes, this means that processes should be considered in which particle number is allowed to vary. Within the context of statistical mechanics, the Gibbsian grandcanonical ensemble is a suitable device for describing such processes. It is shown how the grandcanonical entropy relates in the appropriate way to changes of other thermodynamical quantities in reversible processes, and how the thermodynamical account of the entropy of mixing is recovered even when treating the particles as distinguishable. View Full-Text
Keywords: Gibbs paradox; thermodynamics; extensivity; foundations of statistical mechanics; indistinghuishability; entropy of mixing Gibbs paradox; thermodynamics; extensivity; foundations of statistical mechanics; indistinghuishability; entropy of mixing
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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van Lith, J. The Gibbs Paradox: Lessons from Thermodynamics. Entropy 2018, 20, 328.

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