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On Boltzmann versus Gibbs and the Equilibrium in Statistical Mechanics

Published online by Cambridge University Press:  01 January 2022

Abstract

Charlotte Werndl and Roman 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. This note points out conceptual confusions that could arise from their discussion, concerning, in particular, the authors’ use of “Boltzmann equilibrium.” It also clarifies the status of the Khinchin condition for the equivalence of Boltzmannian and Gibbsian equilibrium predictions and shows that it follows, under the assumptions proposed by Werndl and Frigg, from standard arguments in probability theory.

Type
Discussion
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

I thank the editor, Andrea Woody, anonymous referees, and Charlotte Werndl for feedback that was very helpful in improving the tone and focus of this discussion note. I am also very grateful to Detlef Dürr for helpful comments and discussions.

References

Boltzmann, L. 1896. “Entgegnung auf die wärmetheoretischen Betrachtungen des Hrn. E. Zermelo.” Annalen der Physik 293:773–84.CrossRefGoogle Scholar
Goldstein, S. 2001. “Boltzmann’s Approach to Statistical Mechanics.” In Chance in Physics: Foundations and Perspectives, ed. Bricmont, J. et al., 3954. Berlin: Springer.CrossRefGoogle Scholar
Lavis, D. A. 2005. “Boltzmann and Gibbs: An Attempted Reconciliation.” Studies in History and Philosophy of Science B 36 (2): 245–73..Google Scholar
Lazarovici, D., and Reichert, P.. 2015. “Typicality, Irreversibility and the Status of Macroscopic Laws.” Erkenntnis 80 (4): 689716..CrossRefGoogle Scholar
Werndl, C., and Frigg, R.. 2015a. “Reconceptualising Equilibrium in Boltzmannian Statistical Mechanics and Characterising Its Existence.” Studies in History and Philosophy of Science B 49:1931.CrossRefGoogle Scholar
Werndl, C., and Frigg, R.. 2015b. “Rethinking Boltzmannian Equilibrium.” Philosophy of Science 82 (5): 1224–35..CrossRefGoogle Scholar
Werndl, C., and Frigg, R.. 2017. “Mind the Gap: Boltzmannian versus Gibbsian Equilibrium.” Philosophy of Science 84 (5): 1289–302..CrossRefGoogle Scholar
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