{"paper":{"title":"Entropy, Pressure and Duality for Gibbs plans in Ergodic Transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.OC","math.PR"],"primary_cat":"math.DS","authors_text":"A. O. Lopes, J. K. Mengue, J. Mohr, R. R. Souza","submitted_at":"2013-08-29T16:35:26Z","abstract_excerpt":"Let $X$ be a finite set and $\\Omega=\\{1,...,d\\}^{\\mathbb{N}}$ be the Bernoulli space. Denote by $\\sigma$ the shift map acting on $\\Omega$. For a fixed probability $\\mu$ on $X$ with supp($\\mu$)$=X$, define $\\Pi(\\mu,\\sigma)$ as the set of all Borel probabilities $\\pi \\in P(X\\times \\Omega)$ such that the $x$-marginal of $\\pi$ is $\\mu $ and the $y$-marginal of $\\pi$ is $\\sigma$-invariant. We consider a fixed Lipschitz cost function $c: X \\times \\Omega \\to \\mathbb{R}$ and an associated Ruelle operator. We introduce the concept of Gibbs plan, which is a probability on $X \\times \\Omega$. Moreover, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6514","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}