{
  "abstract": "We introduce a general machinery to study {\\em thermodynamic formalism out of equilibrium}: The thermodynamics of a topological Markov shift (denoted by $Σ^-$) where the potential is given by a random walk on a compact metric space $X$ (and the randomness is driven by a Gibbs process). We introduce the {\\em semi-Ruelle operator}, which acts on $C(Σ^-\\times X)$. We construct conformal measures and harmonic functions for the semi-Ruelle operator. We present a few applications: (1) We provide a new proof to the POE variational principle (POE stands for the {\\em pressure out of equilibrium} which is associated with the process), and we show that maximizing measures in the POE variational principle admit positive {\\em entropy out of equilibrium}, and satisfy {\\em semi-Gibbs estimates}. (2) In the setting where the random walk on the fiber $X$ is given by $C^{1+}$ diffeomorphisms (which are allowed to be very dissipative), and it satisfies the open condition of {\\em effective expansion on average}, we show that the {\\em averaged semi-Ruelle operator} is quasi-compact when acting on a Sobolev function space. An application includes proving a spectral gap when assuming volume decay of correlations, and proving bounds on the dimension of stationary measure in terms of similarity dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12068",
  "author_total": 1,
  "authors": [
    {
      "name": "Snir Ben Ovadia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jf5y43gqzn1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12068",
  "fulltext_url": null,
  "id": "1jf5y43gqzn1g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12068",
  "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",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7212905226",
  "pdf_url": "https://arxiv.org/pdf/2609.12068",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jf5y43gqzn1g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12068",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12068"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Thermodynamic Formalism Out of Equilibrium Part II: Semi-Ruelle Operator, Conformal Measures, and Effective Expansion and Quasi-Compactness",
  "title_text": "Thermodynamic Formalism Out of Equilibrium Part II: Semi-Ruelle Operator, Conformal Measures, and Effective Expansion and Quasi-Compactness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/1jf5y43gqzn1g",
  "venue": "arXiv",
  "versions": []
}