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Mind the Gap: Boltzmannian versus Gibbsian Equilibrium

Published online by Cambridge University Press:  01 January 2022

Charlotte Werndl  and
Roman Frigg
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Abstract

There are two main theoretical frameworks in statistical mechanics, one associated with Boltzmann and the other with Gibbs. Despite their well-known differences, there is a prevailing view that equilibrium values calculated in both frameworks coincide. We show that this is wrong. There are important cases in which the Boltzmannian and Gibbsian equilibrium concepts yield different outcomes. Furthermore, the conditions under which equilibriums exists are different for Gibbsian and Boltzmannian statistical mechanics. There are, however, special circumstances under which it is true that the equilibrium values coincide. We prove a new theorem providing sufficient conditions for this to be the case.

Type
Physical Sciences
Information
Philosophy of Science , Volume 84 , Issue 5 , December 2017 , pp. 1289 - 1302
Copyright
Copyright © The Philosophy of Science Association

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