{"paper":{"title":"Thermodynamic Equilibrium in General Relativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","cond-mat.stat-mech","physics.class-ph"],"primary_cat":"gr-qc","authors_text":"A. Del Popolo (Catania University), A. R. Plastino (CeBio y Departamento de Ciencias Basicas, J. A. S. Lima (Departamento de Astronomia, Universidade de Sao Paulo), Universidad Nacional del Noroeste de la Provincia de Buenos Aires, UNNOBA)","submitted_at":"2019-11-20T17:44:36Z","abstract_excerpt":"The thermodynamic equilibrium condition for a static self-gravitating fluid in the Einstein theory is defined by the Tolman-Ehrenfest temperature law, $T{\\sqrt {g_{00}(x^{i})}} = constant$, according to which the proper temperature depends explicitly on the position within the medium through the metric coefficient $g_{00}(x^{i})$. By assuming the validity of Tolman-Ehrenfest \"pocket temperature\", Klein also proved a similar relation for the chemical potential, namely, $\\mu {\\sqrt {g_{00}(x^{i})}} = constant$. In this letter we prove that a more general relation uniting both quantities holds re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09060","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.09060/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}