{"paper":{"title":"Black hole equations of state and response functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Manus R. Visser, Silvester G.A. Borsboom","submitted_at":"2026-06-15T18:09:18Z","abstract_excerpt":"We systematically develop a framework for equilibrium thermodynamics in terms of thermodynamic representations, which are choices of thermodynamic potential and independent variables, one from each conjugate pair. In each representation, equations of state arise from first derivatives of the potential and response functions from its second derivatives. We apply this framework to ideal gases and to Schwarzschild black holes in a spherical cavity in various representations, interpreting the cavity area and its conjugate surface pressure as the thermodynamic volume and pressure of a holographical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17171","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17171/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"}