{
  "abstract": "We prove Villani's conjecture on entropy production for Kac's walk with uniform collision angles. For every $N\\geq2$, with total collision rate $N$, the optimal entropy production constant is $2/(N-1)$. We show that the known lower bound is sharp by constructing two families of smooth strictly positive probability densities, invariant under coordinate permutations and sign changes. The first consists of normalized products of inverse powers; the second is obtained by conditioning products of Gaussian mixtures on the energy sphere. With $N$ fixed, we compute the leading terms of entropy and entropy production. Successive parameter limits yield two independent proofs of sharpness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22675",
  "author_total": 3,
  "authors": [
    {
      "name": "Fuqing Gao"
    },
    {
      "name": "Shaochen Wang"
    },
    {
      "name": "Xianjie Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/567snhna9tdhj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22675",
  "fulltext_url": null,
  "id": "567snhna9tdhj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22675",
  "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.PR"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7214019858",
  "pdf_url": "https://arxiv.org/pdf/2609.22675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/567snhna9tdhj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Villani's conjecture for Kac's walk",
  "title_text": "Villani's conjecture for Kac's walk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/567snhna9tdhj",
  "venue": "arXiv",
  "versions": []
}