PreprintarXiv licencearXiv
The entropy production is not always monotone for hard spheres or for Maxwell molecules
Abstract
In 1966, McKean asked whether the entropy production of the Boltzmann equation must be monotone decreasing in time. We show that this is not the case even in the space-homogeneous setting for the Boltzmann collision operator with a constant angular cross section and the kinetic parameter γ∈ [0,1]. This recovers the classical case of hard spheres and the simplest case of Maxwell molecules. Our examples are radially symmetric mixtures of Maxwellians.
Related
- The entropy production is not always monotone for the Kac equation
- Global forward self-similar solutions of the spatially inhomogeneous Boltzmann equation for cutoff Maxwell molecules
- Fock-Space Formulation of the Boltzmann Collision Operator for Maxwell Molecules
- Measures of maximal entropy for monotone factors of smooth surface diffeomorphisms
- Perelman's entropy and Gromov-Hausdorff versus dynamical stability of round spheres
BibTeX
@misc{silvestre2026entropy,
title = {{The entropy production is not always monotone for hard spheres or for Maxwell molecules}},
author = {Luis Silvestre},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01753},
eprint = {2609.01753},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01753},
}
RIS
TY - UNPB
TI - The entropy production is not always monotone for hard spheres or for Maxwell molecules
AU - Luis Silvestre
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01753
UR - https://arxiv.org/abs/2609.01753
AB - In 1966, McKean asked whether the entropy production of the Boltzmann equation must be monotone decreasing in time. We show that this is not the case even in the space-homogeneous setting for the Boltzmann collision operator with a constant angular cross section and the kinetic parameter γ∈ [0,1]. This recovers the classical case of hard spheres and the simplest case of Maxwell molecules. Our examples are radially symmetric mixtures of Maxwellians.
ER -