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arXiv · 2604.04861

The entropy production is not always monotone in the space-homogeneous Boltzmann equation

Luis Silvestre
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Abstract

We show an example of a function and a collision kernel for which the entropy production increases in time when we flow it by the space-homogeneous Boltzmann equation. The collision kernel is not any of the physically motivated kernels that are commonly used in the literature. In this particular setting, our result disproves a conjecture of McKean from 1966.

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Luis Silvestre. 2026-04-06. The entropy production is not always monotone in the space-homogeneous Boltzmann equation. https://arxiv.org/abs/2604.04861

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