{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BTYZ4BHYPOFM6G2VSQIRPV565Y","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":"c7b895e298692049fe13b1037f951d7383595a33f84ca008c800be5b67b5a9af","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-10-09T14:22:35Z","title_canon_sha256":"3a217c4e4f7a56963e06429e6af499a9394b9ba8795e741b45939bc5f72134db"},"schema_version":"1.0","source":{"id":"2310.05747","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.05747","created_at":"2026-07-05T06:59:55Z"},{"alias_kind":"arxiv_version","alias_value":"2310.05747v2","created_at":"2026-07-05T06:59:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.05747","created_at":"2026-07-05T06:59:55Z"},{"alias_kind":"pith_short_12","alias_value":"BTYZ4BHYPOFM","created_at":"2026-07-05T06:59:55Z"},{"alias_kind":"pith_short_16","alias_value":"BTYZ4BHYPOFM6G2V","created_at":"2026-07-05T06:59:55Z"},{"alias_kind":"pith_short_8","alias_value":"BTYZ4BHY","created_at":"2026-07-05T06:59:55Z"}],"graph_snapshots":[{"event_id":"sha256:c4c37d1dfed090dad75aea3a34754714e8f34b3b40af2364516ded1c6c87e97a","target":"graph","created_at":"2026-07-05T06:59:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.05747/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent probability density function of the thermodynamic work evolving in the switching time is solved as a special case. From such a relation, I prove Jarzynski's equality and Crook's fluctuation theorem. The particular case of a Gaussian distribution for slowly-varying processes is derived as well at the end.","authors_text":"Pierre Naz\\'e","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-10-09T14:22:35Z","title":"Probability distribution of classical observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.05747","kind":"arxiv","version":2},"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":"sha256:7bb860759135df8b10c27848b988d508ec3d13dd980c8cf4af6f218738835031","target":"record","created_at":"2026-07-05T06:59:55Z","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":"c7b895e298692049fe13b1037f951d7383595a33f84ca008c800be5b67b5a9af","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2023-10-09T14:22:35Z","title_canon_sha256":"3a217c4e4f7a56963e06429e6af499a9394b9ba8795e741b45939bc5f72134db"},"schema_version":"1.0","source":{"id":"2310.05747","kind":"arxiv","version":2}},"canonical_sha256":"0cf19e04f87b8acf1b55941117d7beee2c91378d03788df39f656b659118b04d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cf19e04f87b8acf1b55941117d7beee2c91378d03788df39f656b659118b04d","first_computed_at":"2026-07-05T06:59:55.048949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:59:55.048949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"duRZL5agLoS2P8CQeei3Zz6KhkmKxT229CX+ZjlduaxMl82VuCXeqsSWagkRE3+oYgG6wV2cgIIR1yR/uknZBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:59:55.049406Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.05747","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bb860759135df8b10c27848b988d508ec3d13dd980c8cf4af6f218738835031","sha256:c4c37d1dfed090dad75aea3a34754714e8f34b3b40af2364516ded1c6c87e97a"],"state_sha256":"56237a47745d7412d671f2a0111448e40c811824de92a37e35e07df49cc6a859"}