{
  "abstract": "We investigate the relationship between the dissipation potential $S_{\\mathrm{NB}}$ and information entropy in stochastic Nambu nonequilibrium thermodynamics (NNET). Starting from pure diffusion, gradient-flow systems, and systems with Hamiltonian rotational currents, we derive the stationary distribution of the Fokker--Planck equation including a Nambu flow. We show that, when the Nambu flow preserves the dissipation potential and an Einstein-type relation holds between the diffusion matrix and the transport tensor, the stationary distribution is governed by an exponential weight determined by $S_{\\mathrm{NB}}$. Consequently, the local self-information is directly related to the dissipation potential, demonstrating that $S_{\\mathrm{NB}}$ should not be identified with the Shannon entropy itself but instead serves as the stationary quasipotential governing the nonequilibrium steady-state distribution. Using the distinction between the thermodynamic entropy and the dissipation potential established for an open gas--piston system coupled to a thermal bath and an external-pressure reservoir, we further clarify the Massieu interpretation of $S_{\\mathrm{NB}}$, introduce a Nambu canonical distribution, and derive the covariance of fluctuations within the saddle-point approximation. These results provide a statistical interpretation of the NNET dissipation potential by identifying it as the stationary quasipotential underlying nonequilibrium steady states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03790",
  "author_total": 2,
  "authors": [
    {
      "name": "So Katagiri"
    },
    {
      "name": "Tatsuaki Wada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89gd9wkzpyjxg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03790",
  "fulltext_url": null,
  "id": "89gd9wkzpyjxg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03790",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7220655827",
  "pdf_url": "https://arxiv.org/pdf/2610.03790",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89gd9wkzpyjxg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.03790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03790"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics",
  "title_text": "Information Entropy and Dissipation Potential in Stochastic Nambu Nonequilibrium Thermodynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/89gd9wkzpyjxg",
  "venue": "arXiv",
  "versions": []
}