{
  "abstract": "We introduce a nonlinear Poissonian fluctuating Boltzmann equation whose noise encodes both the fluctuations and the path large-deviation rate function of the underlying hard-sphere gas. Unlike the Gaussian-noise equations commonly studied in fluctuating hydrodynamics, the present equation raises a new difficulty: a Poisson random measure produces jumps that may destroy the nonnegativity of the solution. To address this problem, we construct a finite-dimensional coarse-grained jump process and prove its well-posedness and nonnegativity. For each fixed mesh, this process satisfies a good path large-deviation principle. We then fix a regularized velocity cutoff and study the asymptotic behavior of the discrete rate functions as the mesh is refined. On a class of biased regular paths, their limit is the corresponding cutoff Boltzmann large-deviation rate function associated with the hard-sphere gas. This establishes the consistency of the coarse-grained fluctuating Boltzmann model with the underlying particle system at the level of path large deviations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06482",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhengyan Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ch4tm2qr4p2n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06482",
  "fulltext_url": null,
  "id": "6ch4tm2qr4p2n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06482",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7212078529",
  "pdf_url": "https://arxiv.org/pdf/2609.06482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ch4tm2qr4p2n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Fluctuating Kinetic Theory: A Poissonian Stochastic Boltzmann Equation",
  "title_text": "Fluctuating Kinetic Theory: A Poissonian Stochastic Boltzmann Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/6ch4tm2qr4p2n",
  "venue": "arXiv",
  "versions": []
}