{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:RUGWHQY33R4NQBYTTWBGMJ3D4M","short_pith_number":"pith:RUGWHQY3","schema_version":"1.0","canonical_sha256":"8d0d63c31bdc78d807139d82662763e32de1c1ba4cad3eb14716e73707c66004","source":{"kind":"arxiv","id":"cond-mat/0508089","version":2},"attestation_state":"computed","paper":{"title":"H-Theorems from Autonomous Equations","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"C. Maes, K. Netocny, W. De Roeck","submitted_at":"2005-08-03T11:30:42Z","abstract_excerpt":"The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy.\n  If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autono"},"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":"cond-mat/0508089","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-08-03T11:30:42Z","cross_cats_sorted":[],"title_canon_sha256":"0804f994e6bce570bf1bf1478ec68d31da71bd160a3814135b5202256f3f50fc","abstract_canon_sha256":"98f346964f5718ce9d2a44a306e95af22a235b7df813fdc0b8acdb31e25698ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:50.569901Z","signature_b64":"+F7qNBjUbtcMAev516y9fzF3Ch04ZvAGt9l3v/P28XE4P5cpbMeynkcSX2qcH0iIVpcZaLQ0TwMupQ+Cbs3jBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d0d63c31bdc78d807139d82662763e32de1c1ba4cad3eb14716e73707c66004","last_reissued_at":"2026-05-18T01:39:50.569182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:50.569182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"H-Theorems from Autonomous Equations","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"C. Maes, K. Netocny, W. De Roeck","submitted_at":"2005-08-03T11:30:42Z","abstract_excerpt":"The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy.\n  If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0508089","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":""},"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":"cond-mat/0508089","created_at":"2026-05-18T01:39:50.569297+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0508089v2","created_at":"2026-05-18T01:39:50.569297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0508089","created_at":"2026-05-18T01:39:50.569297+00:00"},{"alias_kind":"pith_short_12","alias_value":"RUGWHQY33R4N","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"RUGWHQY33R4NQBYT","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"RUGWHQY3","created_at":"2026-05-18T12:25:53.335082+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/RUGWHQY33R4NQBYTTWBGMJ3D4M","json":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M.json","graph_json":"https://pith.science/api/pith-number/RUGWHQY33R4NQBYTTWBGMJ3D4M/graph.json","events_json":"https://pith.science/api/pith-number/RUGWHQY33R4NQBYTTWBGMJ3D4M/events.json","paper":"https://pith.science/paper/RUGWHQY3"},"agent_actions":{"view_html":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M","download_json":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M.json","view_paper":"https://pith.science/paper/RUGWHQY3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0508089&json=true","fetch_graph":"https://pith.science/api/pith-number/RUGWHQY33R4NQBYTTWBGMJ3D4M/graph.json","fetch_events":"https://pith.science/api/pith-number/RUGWHQY33R4NQBYTTWBGMJ3D4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M/action/storage_attestation","attest_author":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M/action/author_attestation","sign_citation":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M/action/citation_signature","submit_replication":"https://pith.science/pith/RUGWHQY33R4NQBYTTWBGMJ3D4M/action/replication_record"}},"created_at":"2026-05-18T01:39:50.569297+00:00","updated_at":"2026-05-18T01:39:50.569297+00:00"}