{
  "abstract": "Links between physicals systems and computability properties have been an active field of investigation in recent years. Inspired by a previous work in the context of positive temperature Gibbs measures, we prove here that in the context of zero-temperature ergodic optimisation, for a computable potential and provided with several reasonable assumptions, the maximum ergodic average is a computable real number, and the set of maximising measures is a $Π_1$-computable compact set. Then, in the more specific context of symbolic dynamics, with finite-range interactions on subshifts of finite type, we provide an explicit algorithm to compute both the maximum ergodic average and the set of maximising measures in finite time, with a matching code repository.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11404",
  "author_total": 2,
  "authors": [
    {
      "name": "Léopoldine Gayral"
    },
    {
      "name": "Mathieu Hoyrup"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fw7q2sd1mtm6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11404",
  "fulltext_url": null,
  "id": "fw7q2sd1mtm6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11404",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.LO"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7168265220",
  "pdf_url": "https://arxiv.org/pdf/2607.11404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fw7q2sd1mtm6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2607.11404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Computable Ergodic Optimisation",
  "title_text": "Computable Ergodic Optimisation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/fw7q2sd1mtm6x",
  "venue": "arXiv",
  "versions": []
}