{"paper":{"title":"The effective potential and transshipment in thermodynamic formalism at temperature zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Eduardo Garibaldi","submitted_at":"2010-08-05T19:11:14Z","abstract_excerpt":"Denote the points in {1,2,..,r}^{Z}= {1,2,..,r}^{N} x {1,2,..,r}^{N} by ({y}^*, {x}). Given a Lipschitz continuous observable A: {1,2,..,r}^{Z} \\to {R} , we define the map {G}^+: {H}\\to {H} by {G}^+(\\phi)({y}^*) = \\sup_{\\mu \\in {M}_\\sigma} [\\int_{\\{1,2,..,r\\}^{N}} ( A({y}^*, {x}) + \\phi({x})) d\\mu({x}) + h_\\mu(\\sigma) ], where: \\sigma is the left shift map acting on {1,2,..,r}^{N}; {M}_\\sigma denotes the set of \\sigma-invariant Borel probabilities; h_\\mu(\\sigma) indicates the Kolmogorov-Sinai entropy; {H } is the Banach space of Lipschitz real-valued functions on {1,2,..,r}^{N}. We show there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1042","kind":"arxiv","version":1},"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"}