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2018

On Boltzmann vs. Gibbs and the Equilibrium in Statistical Mechanics

Lazarovici, Dustin

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In a recent article, Werndl and Frigg discuss the relationship between the Boltzmannian and Gibbsian framework of statistical mechanics, addressing in particular the question when equilibrium values calculated in both frameworks agree.

In this paper, I address conceptual confusions that could arise from their discussion, concerning in particular the authors' use of "Boltzmann equilibrium".
I also clarify the status of the Khinchin condition for the equivalence of Boltzmannian and Gibbsian, and show that it follows under the assumptions proposed by Werndl and Frigg from standard arguments in probability theory.

On Boltzmann vs. Gibbs and the Equilibrium in Statistical Mechanics · Around

Built on

Boltzmann’s Approach to Statistical Mechanics
Goldstein, S. (2001) · 2001
Earlier work this paper cites.
Boltzmann and Gibbs: An attempted reconciliation
Lavis, D. A. (2005, June) · 2005
Earlier work this paper cites.

Similar

Typicality, irreversibility and the status of macroscopic laws
Lazarovici, D. and P. Reichert (2015) · 2015
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Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E. Zermelo
Boltzmann, L. (1896)
Cited in the paper.
Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence
Werndl, C. and R. Frigg (2015a)
Cited in the paper.
Rethinking Boltzmannian Equilibrium
Werndl, C. and R. Frigg (2015b)
Cited in the paper.

Then

Mind the Gap: Boltzmannian versus Gibbsian Equilibrium
Werndl, C. and R. Frigg (2017, July) · 2017
Later among the works it cites.

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