{
  "abstract": "This paper investigates the canonical Koszul one-form at the interface of Jean Marie Souriau's Lie group thermodynamics and Paulette Libermann's symplectically complete foliations to describe geometric dissipation. On the Poincaré half-plane $\\mathbb{H}$ under $SL(2, \\mathbb{R})$, the equivariant momentum map level sets form a regular Libermann foliation framing the conservative boundaries. The Koszul-derived dissipative vector field acts strictly transverse to these leaves, driving a metriplectic flow that breaks Noether conservation laws and generates entropy. Quantum wise, we develop Berezin quantization on para-Kähler symmetric spaces, where the Koszul potential acts as a weight determining state density via the Fisher Souriau metric, and formalize Kostant's geometric quantization using the real dual polarizations of a bi-Lagrangian web.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30976",
  "author_total": 5,
  "authors": [
    {
      "name": "Prosper Rosaire Mama Assandje"
    },
    {
      "name": "Frédéric Barbaresco"
    },
    {
      "name": "Romain Nimpa Pefoukeu"
    },
    {
      "name": "Michel Bertrand Djiadeu Ngaha"
    },
    {
      "name": "Nozah Mba Frankel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7p6rdthdaqhzw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30976",
  "fulltext_url": null,
  "id": "7p6rdthdaqhzw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30976",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214654714",
  "pdf_url": "https://arxiv.org/pdf/2609.30976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7p6rdthdaqhzw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Geometric Dissipation Structures and the Koszul Form",
  "title_text": "Geometric Dissipation Structures and the Koszul Form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/7p6rdthdaqhzw",
  "venue": "arXiv",
  "versions": []
}