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Mind the Gap: Boltzmannian versus Gibbsian Equilibrium

Werndl, Charlotte and Frigg, Roman (2017) Mind the Gap: Boltzmannian versus Gibbsian Equilibrium. [Preprint]

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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 where the Boltzmannian and Gibbsian equilibrium concepts yield different outcomes. Furthermore, the conditions under which equilibria 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 suffcient conditions for this to be the case.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Werndl, Charlottecharlotte.werndl@sbg.ac.at
Frigg, Romanr.p.frigg@lse.ac.uk
Keywords: Gibbs, Boltzmann, Equilibrium, baker’s gas, Ising model
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Roman Frigg
Date Deposited: 31 Jul 2017 00:46
Last Modified: 31 Jul 2017 00:46
Item ID: 13269
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: January 2017
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/13269

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