{
  "abstract": "Large deviation theory lacks a geometric foundation for its rate functions and fluctuation symmetries. This paper develops a contact large deviation theory on stochastic vector bundles, in which the rate function, the scaled cumulant generating function, and a Gallavotti--Cohen-type fluctuation duality all follow from the contact 1-form. The constraint function acts as a generalized Lagrangian; the least constraint principle yields the dynamics, and the contact potential is built order by order from the master equation, producing a coupled Hamilton--Jacobi--transport system governed by the invariant density, drift, and fluctuation tensor. The contact path measure satisfies a large deviation principle with rate function given by the constraint action; the scaled cumulant generating function obeys a stationary eigenvalue equation with a Donsker--Varadhan variational characterization. The entropy production rate, the fluctuation--dissipation combination $e=\\tfrac12 g^T Ag-σ$, is the physical observable; the time-reversal involution $J:(t,y,ϕ)\\mapsto(t,y,-ϕ-\\nabla\\lnρ)$ with reversed drift $v^{\\mathrm{rev}}=-v+Ag$ yields a Gallavotti--Cohen-type duality $λ_{\\mathrm{fwd}}(q)=λ_{\\mathrm{rev}}(q+1)+λ_{\\mathrm{fwd}}(-1)$. The classical one-dimensional GC symmetry is recovered in the reversible case $Ag=0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19679",
  "author_total": 1,
  "authors": [
    {
      "name": "D. Y. Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9ex17x2sw3kh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19679",
  "fulltext_url": null,
  "id": "d9ex17x2sw3kh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19679",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19679",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9ex17x2sw3kh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19679",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19679"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Contact Large Deviations of Stochastic Vector Bundles",
  "title_text": "Contact Large Deviations of Stochastic Vector Bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/d9ex17x2sw3kh",
  "venue": "arXiv",
  "versions": []
}