{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:VNWD6W3673KGLRX5MV37ACWTAQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3be2fd55158d9dde94fdbd390d93c8a2284c27906cf1cc2db86d63308cf7aad3","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-06-17T20:00:10Z","title_canon_sha256":"0a90b538002e234454c54b57dc5d4ee4eed8c9b072631dfaec8162a126b1d2a0"},"schema_version":"1.0","source":{"id":"0806.2862","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.2862","created_at":"2026-05-18T03:49:10Z"},{"alias_kind":"arxiv_version","alias_value":"0806.2862v8","created_at":"2026-05-18T03:49:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.2862","created_at":"2026-05-18T03:49:10Z"},{"alias_kind":"pith_short_12","alias_value":"VNWD6W3673KG","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"VNWD6W3673KGLRX5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"VNWD6W36","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:4c7bc4bd2356f00dd46a50ed627e51bc00267f8843ca5673033e4f380c2f5d22","target":"graph","created_at":"2026-05-18T03:49:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We define a diagonal entropy (d-entropy) for an arbitrary Hamiltonian system as $S_d=-\\sum_n \\rho_{nn}\\ln \\rho_{nn}$ with the sum taken over the basis of instantaneous energy states. In equilibrium this entropy coincides with the conventional von Neumann entropy $S_n=-{\\rm Tr}\\, \\rho\\ln\\rho$. However, in contrast to $S_n$, the d-entropy is not conserved in time in closed Hamiltonian systems. If the system is initially in stationary state then in accord with the second law of thermodynamics the d-entropy can only increase or stay the same. We also show that the d-entropy can be expressed throug","authors_text":"Anatoli Polkovnikov","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-06-17T20:00:10Z","title":"Microscopic diagonal entropy and its connection to basic thermodynamic relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.2862","kind":"arxiv","version":8},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:828053defcf6369434feefb0bdc0997a3d34bb5d359c633a479310cd58ea45b3","target":"record","created_at":"2026-05-18T03:49:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3be2fd55158d9dde94fdbd390d93c8a2284c27906cf1cc2db86d63308cf7aad3","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-06-17T20:00:10Z","title_canon_sha256":"0a90b538002e234454c54b57dc5d4ee4eed8c9b072631dfaec8162a126b1d2a0"},"schema_version":"1.0","source":{"id":"0806.2862","kind":"arxiv","version":8}},"canonical_sha256":"ab6c3f5b7efed465c6fd6577f00ad3041de146b24132838f3c64e83701008ba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab6c3f5b7efed465c6fd6577f00ad3041de146b24132838f3c64e83701008ba8","first_computed_at":"2026-05-18T03:49:10.656754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:10.656754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rzk141QMhooWGN31hWKi8Mxr4xEV150yG4D4SCG9M5KIZ7J9BUzTK49OOpDT5/ZbDof9uBli64zDE9Vq1BpTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:10.657262Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.2862","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:828053defcf6369434feefb0bdc0997a3d34bb5d359c633a479310cd58ea45b3","sha256:4c7bc4bd2356f00dd46a50ed627e51bc00267f8843ca5673033e4f380c2f5d22"],"state_sha256":"cc029285202a6066d5e223e6237795f71f2af12941fcb36f2a9ff2878ebbe20e"}