{
  "abstract": "We introduce a geometric decomposition of the hard-sphere partition function. Using a close-packing-inspired geometric bound on the available insertion volume, made rigorous when a corresponding local density certificate is available, we establish a reference upper bound $Q^\\ast$ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function found by Speedy yields a new form for the $d$-dimensional partition function, $Q(N,V,T)=Q^\\ast \\exp(-N \\mathcal{J})$, where $\\mathcal{J}$ depends strictly on the boundary-to-volume ratio of the voids and the close-packing density. Overall, this work provides an exact reformulation of hard-sphere thermodynamics, thus deepening our statistical geometric understanding of hard spheres.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16483",
  "author_total": 1,
  "authors": [
    {
      "name": "Luke K. Davis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6q1ryjrjb2z7q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16483",
  "fulltext_url": null,
  "id": "6q1ryjrjb2z7q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16483",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
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      "arxiv",
      "math-ph"
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      "arxiv",
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      "1606|Advanced Physical and Chemical Molecular Interactions"
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  "openalex": "W7164922542",
  "pdf_url": "https://arxiv.org/pdf/2606.16483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6q1ryjrjb2z7q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:53Z",
      "native_id": "2606.16483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Geometric decomposition of the d-dimensional hard-sphere partition function",
  "title_text": "Geometric decomposition of the d-dimensional hard-sphere partition function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/6q1ryjrjb2z7q",
  "venue": "arXiv",
  "versions": []
}