{
  "abstract": "We study the equilibrium statistical mechanics of one-dimensional classical Machian fractons: particles whose dynamics conserves a global dipole moment and whose Hamiltonian couples momentum differences through a position-dependent pair-inertia kernel. Compactly supported interaction kernels have a divergence in the Gibbs partition function, and have been shown to break ergodicity and symmetry by forming non-equilibrium steady states with particle clusters, evading the Hohenberg-Mermin-Wagner-Coleman theorem. In this paper, we consider kernels with non-compact support and study their ergodic properties. For exponentially decaying kernels, graph-Laplacian and matrix-tree bounds provide an extensive free energy suggesting that a putative statistical mechanical description is valid. Similarly, uniform non-local kernels have a super-extensive free energy and require a Kac rescaling. A generalized Hohenberg--Mermin--Wagner--Coleman argument, supported by finite-size scaling, implies symmetry-breaking density order parameter vanishes at all wave vectors melting the long-range translation-breaking density order of compact kernels. To study the resulting equilibrium ensemble, we construct a nonreversible event-chain Monte Carlo (ECMC) algorithm that samples the coupled position-momentum phase space while preserving the dipole moment and total momentum. The ECMC sampling is shown to quantitatively match long time-averaged quantites in Hamiltonian dynamics. The equilibrium liquid exhibits preferred short-range clustering and strongly non-Gaussian single-particle momentum tails associated with the correlated nature of positions and momenta. This paper provides a detailed investigation into the equilibrium liquid properties of the non-compact regime, whilst the companion paper investigates the mechanisms that relax the liquid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25999",
  "author_total": 3,
  "authors": [
    {
      "name": "Ylias Sadki"
    },
    {
      "name": "Abhishodh Prakash"
    },
    {
      "name": "S. L. Sondhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4r9n41sbb35j4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25999",
  "fulltext_url": null,
  "id": "4r9n41sbb35j4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25999",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25999",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4r9n41sbb35j4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25999",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25999"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Statistical mechanics of classical fractons on a line",
  "title_text": "Statistical mechanics of classical fractons on a line",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/4r9n41sbb35j4",
  "venue": "arXiv",
  "versions": []
}