Foundations of Physics

, Volume 47, Issue 4, pp 471–489 | Cite as

Irreversibility in the Derivation of the Boltzmann Equation

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Abstract

Uffink and Valente (Found Phys 45:404–438, 2015) claim that there is no time-asymmetric ingredient that, added to the Hamiltonian equations of motion, allows to obtain the Boltzmann equation within the Lanford’s derivation. This paper is a discussion and a reply to that analysis. More specifically, I focus on two mathematical tools used in this derivation, viz. the Boltzmann–Grad (B–G) limit and the incoming configurations. Although none of them are time-asymmetric ingredients, by themselves, I claim that the use of incoming configurations, as taken within the B–G limit, is such a time-asymmetric ingredient. Accordingly, this leads to reconsider a kind of Stoßzahlansatz within Lanford’s derivation.

Keywords

Boltzmann equation Lanford’s theorem Boltzmann–Grad limit Irreversibility Time-reversal invariance Stoßzahlansatz 

Notes

Acknowledgements

Earlier versions of this article were presented at the 25th biennial meeting of the Philosophy of Science Association, the 18th UK and European Conference on Foundations of Physics, and the British Society for the Philosophy of Science 2016 annual conference. I wish to thank the participants for their helpful comments. I am also grateful to Anouk Barberousse for her insightful comments and the organization of workshops at Sciences, Normes, Decision (FRE 3593, CNRS & Université Paris-Sorbonne) that allow me to discuss this work. Thank you in particular to Sorin Bangu, Nicolas Fillion, Cyrille Imbert, Johannes Lenhard, Robert Moir, and Jos Uffink for comments and discussions. I am also most grateful to Giovanni Valente and Laure Saint-Raymond for their comments on previous drafts of this paper and their contribution to enhancing the quality of the article. This work was supported by “MOVE-IN Louvain” Incoming Post-doctoral Fellowship, co-funded by the Marie Curie Actions of the European Commission.

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institut Supérieur de Philosophie, Université catholique de LouvainLouvain-la-NeuveBelgium

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