{
  "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 $γ\\in [0,1]$. This recovers the classical case of hard spheres and the simplest case of Maxwell molecules. Our examples are radially symmetric mixtures of Maxwellians.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01753",
  "author_total": 1,
  "authors": [
    {
      "name": "Luis Silvestre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ay2fyfmrj1asm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01753",
  "fulltext_url": null,
  "id": "ay2fyfmrj1asm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01753",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
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      "arxiv",
      "math.MP"
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      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
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  "openalex": "W7207829101",
  "pdf_url": "https://arxiv.org/pdf/2609.01753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ay2fyfmrj1asm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01753"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The entropy production is not always monotone for hard spheres or for Maxwell molecules",
  "title_text": "The entropy production is not always monotone for hard spheres or for Maxwell molecules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/ay2fyfmrj1asm",
  "venue": "arXiv",
  "versions": []
}