{
  "abstract": "We develop a geometric framework in which classical thermodynamics is reformulated as a Hamiltonian dynamical system. An explicit canonical mapping $(q,p,t,H)\\leftrightarrow(V,-P,S,-T)$ identifies Maxwell's relations as the characteristic equations of the thermodynamic Poincaré--Cartan one-form, in direct parallel with Hamilton's equations of motion. Treating thermodynamic potentials as action functionals, a variational principle recovers both the Maxwell relations and the thermodynamic constraints (adiabaticity, isothermality) as conserved first integrals. For adiabatic processes in an ideal gas, this yields explicit second-order ordinary differential equations for $V(T)$ and $P(T)$, each governed by a temperature-dependent Lagrangian. Assembling the component Lagrangians into a multi-parameter Lagrangian 1-form $\\mathcal{L}$, we prove that the closure condition $d\\mathcal{L}=0$ holds on the solution manifold, establishing that path-independence of thermodynamic state functions is a geometric consequence of multi-time integrability rather than an independent postulate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18215",
  "author_total": 1,
  "authors": [
    {
      "name": "Sikarin Yoo-Kong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e7r775bjxz7s6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18215",
  "fulltext_url": null,
  "id": "e7r775bjxz7s6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18215",
  "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",
      "nlin.SI"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7213502603",
  "pdf_url": "https://arxiv.org/pdf/2609.18215",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e7r775bjxz7s6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.18215",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18215"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Maxwell's relations as Hamilton's equations: a symplectic and variational framework",
  "title_text": "Maxwell's relations as Hamilton's equations: a symplectic and variational framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/e7r775bjxz7s6",
  "venue": "arXiv",
  "versions": []
}