{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ICF4L2VVVFQO5UQNLDSXYYRAHG","short_pith_number":"pith:ICF4L2VV","canonical_record":{"source":{"id":"1309.4727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-17T17:12:30Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"1cf4c215722e2af08bc9754ea380e06ea97a474f51f066afaea35e31df5fd734","abstract_canon_sha256":"dd72cf3d789853e46cacaf3c12100bfe887633769325dd5f1f6f8be699cfe8b2"},"schema_version":"1.0"},"canonical_sha256":"408bc5eab5a960eed20d58e57c622039b23721c1dc9744c2b60428b818563f76","source":{"kind":"arxiv","id":"1309.4727","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4727","created_at":"2026-05-18T01:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4727v1","created_at":"2026-05-18T01:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4727","created_at":"2026-05-18T01:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"ICF4L2VVVFQO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ICF4L2VVVFQO5UQN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ICF4L2VV","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ICF4L2VVVFQO5UQNLDSXYYRAHG","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-17T17:12:30Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"1cf4c215722e2af08bc9754ea380e06ea97a474f51f066afaea35e31df5fd734","abstract_canon_sha256":"dd72cf3d789853e46cacaf3c12100bfe887633769325dd5f1f6f8be699cfe8b2"},"schema_version":"1.0"},"canonical_sha256":"408bc5eab5a960eed20d58e57c622039b23721c1dc9744c2b60428b818563f76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:47:35.790898Z","signature_b64":"nRY7m1izfJE3eMKvuGH0CYhzK9d5z2qbMHY1V8fnbJ/EglmnYbWran72Tq7+ldFgn6NpCGMVMAYvg2caXEnJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"408bc5eab5a960eed20d58e57c622039b23721c1dc9744c2b60428b818563f76","last_reissued_at":"2026-05-18T01:47:35.790241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:47:35.790241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4727","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hUxlHtti5hiP4LKZe1C3EAnsOJK9lT7b1eSfIRJ79/m65+H0Pl5onjuDEFZidPj5K+Cz/26GC4udfeYe/T96Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:55:18.659251Z"},"content_sha256":"2e9fbd9cdfe5a4a371cde6a44eec04c59e3fbf756929129eb1f27f7f060998a4","schema_version":"1.0","event_id":"sha256:2e9fbd9cdfe5a4a371cde6a44eec04c59e3fbf756929129eb1f27f7f060998a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ICF4L2VVVFQO5UQNLDSXYYRAHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dissipation, interaction and relative entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Gaveau, L. Granger, L. S. Schulman, M. Moreau","submitted_at":"2013-09-17T17:12:30Z","abstract_excerpt":"Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4727","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zf7XWfGcXhJgakf1yvj1N9elz0uG787Ou2yxvBNuZ7zliTtTruskiwOb/M12PGVR7/jWtHpJeRnhRD6HZh7JBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:55:18.659602Z"},"content_sha256":"e8ae38fe4b91cd5bea2b2ccde67a73c8f8bd0684165e019273b7a88c71012885","schema_version":"1.0","event_id":"sha256:e8ae38fe4b91cd5bea2b2ccde67a73c8f8bd0684165e019273b7a88c71012885"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG/bundle.json","state_url":"https://pith.science/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T10:55:18Z","links":{"resolver":"https://pith.science/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG","bundle":"https://pith.science/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG/bundle.json","state":"https://pith.science/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ICF4L2VVVFQO5UQNLDSXYYRAHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ICF4L2VVVFQO5UQNLDSXYYRAHG","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":"dd72cf3d789853e46cacaf3c12100bfe887633769325dd5f1f6f8be699cfe8b2","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-17T17:12:30Z","title_canon_sha256":"1cf4c215722e2af08bc9754ea380e06ea97a474f51f066afaea35e31df5fd734"},"schema_version":"1.0","source":{"id":"1309.4727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4727","created_at":"2026-05-18T01:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4727v1","created_at":"2026-05-18T01:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4727","created_at":"2026-05-18T01:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"ICF4L2VVVFQO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ICF4L2VVVFQO5UQN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ICF4L2VV","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:e8ae38fe4b91cd5bea2b2ccde67a73c8f8bd0684165e019273b7a88c71012885","target":"graph","created_at":"2026-05-18T01:47:35Z","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":"Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a. Kullback-Leibler divergence). The processes considered are general time evolutions both in classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.","authors_text":"B. Gaveau, L. Granger, L. S. Schulman, M. Moreau","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-17T17:12:30Z","title":"Dissipation, interaction and relative entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4727","kind":"arxiv","version":1},"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":"sha256:2e9fbd9cdfe5a4a371cde6a44eec04c59e3fbf756929129eb1f27f7f060998a4","target":"record","created_at":"2026-05-18T01:47:35Z","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":"dd72cf3d789853e46cacaf3c12100bfe887633769325dd5f1f6f8be699cfe8b2","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-17T17:12:30Z","title_canon_sha256":"1cf4c215722e2af08bc9754ea380e06ea97a474f51f066afaea35e31df5fd734"},"schema_version":"1.0","source":{"id":"1309.4727","kind":"arxiv","version":1}},"canonical_sha256":"408bc5eab5a960eed20d58e57c622039b23721c1dc9744c2b60428b818563f76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"408bc5eab5a960eed20d58e57c622039b23721c1dc9744c2b60428b818563f76","first_computed_at":"2026-05-18T01:47:35.790241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:35.790241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nRY7m1izfJE3eMKvuGH0CYhzK9d5z2qbMHY1V8fnbJ/EglmnYbWran72Tq7+ldFgn6NpCGMVMAYvg2caXEnJDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:35.790898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e9fbd9cdfe5a4a371cde6a44eec04c59e3fbf756929129eb1f27f7f060998a4","sha256:e8ae38fe4b91cd5bea2b2ccde67a73c8f8bd0684165e019273b7a88c71012885"],"state_sha256":"30b167b372442ebf6af7ae28fdc1109f4204ef54b1a5d8e0a6b56c1b10aeabcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g/v/ab0W8g2lyrbGoNUuRcaa8wEQlA8O4DOfNsazOzNDsWwnlbjTpYcmrhYpRz4BGza9fGFQmDo2+0QGXEPKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:55:18.661475Z","bundle_sha256":"2968947362c3e0171599ef7f178e7383f8b906372af0180486ab72082762104c"}}