{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QUITCGDBK5RHNN2KZBKYDHCA3I","short_pith_number":"pith:QUITCGDB","schema_version":"1.0","canonical_sha256":"8511311861576276b74ac855819c40da360b6330fd5605d419eed9702e9d916b","source":{"kind":"arxiv","id":"1005.2985","version":5},"attestation_state":"computed","paper":{"title":"Thermal time and the Tolman-Ehrenfest effect: temperature as the \"speed of time\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"gr-qc","authors_text":"Carlo Rovelli, Matteo Smerlak","submitted_at":"2010-05-17T17:37:32Z","abstract_excerpt":"The notion of thermal time has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we study this notion in the restricted context of stationary spacetimes. We show that the Tolman-Ehrenfest effect (in a stationary gravitational field, temperature is not constant in space at thermal equilibrium) can be derived very simply by applying the equivalence principle to a key property of thermal time: at equilibrium, temperature is the rate of thermal time with respect to proper time - the `speed of (thermal) time'. Unlike other published derivations of the Tolman-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1005.2985","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-17T17:37:32Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"2676ac5c8a7474abd1119fd2e02f6f5f1af314a90e48e094390078f5709c2a4c","abstract_canon_sha256":"e7322727982d2460ba52d0e22427d41e8b472f83707057deeb244bdd03fc2676"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:56.588202Z","signature_b64":"zVzjY5H/ev9RHLmRkIjyYWRV0HB7CiD7RrALYDgDx0wPKKBp/iv3yZtyjqOtKKgPXzitrTR+pfGPeIyySpLJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8511311861576276b74ac855819c40da360b6330fd5605d419eed9702e9d916b","last_reissued_at":"2026-05-18T04:26:56.587786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:56.587786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thermal time and the Tolman-Ehrenfest effect: temperature as the \"speed of time\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"gr-qc","authors_text":"Carlo Rovelli, Matteo Smerlak","submitted_at":"2010-05-17T17:37:32Z","abstract_excerpt":"The notion of thermal time has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we study this notion in the restricted context of stationary spacetimes. We show that the Tolman-Ehrenfest effect (in a stationary gravitational field, temperature is not constant in space at thermal equilibrium) can be derived very simply by applying the equivalence principle to a key property of thermal time: at equilibrium, temperature is the rate of thermal time with respect to proper time - the `speed of (thermal) time'. Unlike other published derivations of the Tolman-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2985","kind":"arxiv","version":5},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1005.2985","created_at":"2026-05-18T04:26:56.587851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.2985v5","created_at":"2026-05-18T04:26:56.587851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2985","created_at":"2026-05-18T04:26:56.587851+00:00"},{"alias_kind":"pith_short_12","alias_value":"QUITCGDBK5RH","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"QUITCGDBK5RHNN2K","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"QUITCGDB","created_at":"2026-05-18T12:26:13.927090+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I","json":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I.json","graph_json":"https://pith.science/api/pith-number/QUITCGDBK5RHNN2KZBKYDHCA3I/graph.json","events_json":"https://pith.science/api/pith-number/QUITCGDBK5RHNN2KZBKYDHCA3I/events.json","paper":"https://pith.science/paper/QUITCGDB"},"agent_actions":{"view_html":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I","download_json":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I.json","view_paper":"https://pith.science/paper/QUITCGDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.2985&json=true","fetch_graph":"https://pith.science/api/pith-number/QUITCGDBK5RHNN2KZBKYDHCA3I/graph.json","fetch_events":"https://pith.science/api/pith-number/QUITCGDBK5RHNN2KZBKYDHCA3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I/action/storage_attestation","attest_author":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I/action/author_attestation","sign_citation":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I/action/citation_signature","submit_replication":"https://pith.science/pith/QUITCGDBK5RHNN2KZBKYDHCA3I/action/replication_record"}},"created_at":"2026-05-18T04:26:56.587851+00:00","updated_at":"2026-05-18T04:26:56.587851+00:00"}