{
  "abstract": "We investigate martingale properties of heat dissipated by generic non-equilibrium overdamped Langevin dynamics with multiple dimensions and transport coefficients that may depend explicitly on time and/or space. We find quantitative criteria that establish that heat dissipation may exhibit transient martingale (time-conserved), submartingale (time increasing), and supermartingale (time decreasing) properties in Langevin dynamics with drift coefficients with spatial non-linear dependencies. Furthermore, we reveal a tight link between the heat statistics at stopping (e.g. first-passage) times with that of a functional quantifying the phase-space contraction in the system dynamics. The theoretical results are used to predict the statistical properties of the heat dissipated by a spherical microscopic particle subject to gravity and double-layer forces and hydrodynamically interacting with a rigid wall, whose validity is confirmed by numerical simulations. These results extend the scope of stochastic energetics by revealing a non-trivial relation between heat fluctuations' statistical properties and the non-linear features of non-equilibrium processes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20681",
  "author_total": 3,
  "authors": [
    {
      "name": "Jing Qin"
    },
    {
      "name": "Nariya Uchida"
    },
    {
      "name": "Édgar Roldán"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2k8mkpebzt1j1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20681",
  "fulltext_url": null,
  "id": "2k8mkpebzt1j1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20681",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7213604227",
  "pdf_url": "https://arxiv.org/pdf/2609.20681",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2k8mkpebzt1j1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20681",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20681"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Martingale theory for heat and phase-space contraction in heterogeneous diffusions",
  "title_text": "Martingale theory for heat and phase-space contraction in heterogeneous diffusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/2k8mkpebzt1j1",
  "venue": "arXiv",
  "versions": []
}