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Irreversibility in the derivation of the Boltzmann equation

Abstract : Uffink and Valente (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 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 Boltzmann-Grad limit, is such a time-asymmetric ingredient. Accordingly, this leads to reconsider a kind of Stoßzahlansatz within Lanford's derivation.
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https://hal.archives-ouvertes.fr/hal-01918274
Contributor : Vincent Ardourel <>
Submitted on : Saturday, November 10, 2018 - 3:16:37 PM
Last modification on : Thursday, March 4, 2021 - 8:46:03 AM
Long-term archiving on: : Monday, February 11, 2019 - 1:00:31 PM

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  • HAL Id : hal-01918274, version 1

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Vincent Ardourel. Irreversibility in the derivation of the Boltzmann equation. Foundations of Physics, Springer Verlag, 2017, 47 (4), pp.471-489. ⟨hal-01918274⟩

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