{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7OYRJZ7DEW5GGOPCPBGIZC5B7C","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":"da6a04979ee6e7a770221ba73b2bb22e58ee15b69beee503f149b2a5d26d6dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-04T20:12:36Z","title_canon_sha256":"93f6d27187c011a0017b2e704c94a5a1f3a5b7bdd8e8a4b9fef83b34a30e0b76"},"schema_version":"1.0","source":{"id":"1212.0844","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0844","created_at":"2026-05-18T02:55:36Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0844v5","created_at":"2026-05-18T02:55:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0844","created_at":"2026-05-18T02:55:36Z"},{"alias_kind":"pith_short_12","alias_value":"7OYRJZ7DEW5G","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7OYRJZ7DEW5GGOPC","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7OYRJZ7D","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:e0bca927d7bb689471020a1b80c1313474deeef8fec4bface37e45e84143a910","target":"graph","created_at":"2026-05-18T02:55:36Z","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 the {\\it violation fraction} $\\nu$ as the cumulative fraction of time that the entropy change is negative during single realizations of processes in phase space. This quantity depends both on the number of degrees of freedom $N$ and the duration of the time interval $\\tau$. In the large-$\\tau$ and large-$N$ limit we show that, for ergodic and microreversible systems, the mean value of $\\nu$ scales as $\\langle\\nu(N,\\tau)\\rangle\\sim\\big(\\tau N^{\\frac{1}{1+\\alpha}}\\big)^{-1}$. The exponent $\\alpha$ is positive and generally depends on the protocol for the external driving forces, being ","authors_text":"Daniel Dom\\'inguez, Reinaldo Garc\\'ia-Garc\\'ia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-04T20:12:36Z","title":"Duration of local violations of the second law of thermodynamics along single trajectories in phase space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0844","kind":"arxiv","version":5},"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":"sha256:75534ca0bcc1cf75dd0b3e5e34e3c64373a04af87d3096b57e833d87bedce574","target":"record","created_at":"2026-05-18T02:55:36Z","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":"da6a04979ee6e7a770221ba73b2bb22e58ee15b69beee503f149b2a5d26d6dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-04T20:12:36Z","title_canon_sha256":"93f6d27187c011a0017b2e704c94a5a1f3a5b7bdd8e8a4b9fef83b34a30e0b76"},"schema_version":"1.0","source":{"id":"1212.0844","kind":"arxiv","version":5}},"canonical_sha256":"fbb114e7e325ba6339e2784c8c8ba1f882dac0d40266adf7eae5fd00df3db879","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbb114e7e325ba6339e2784c8c8ba1f882dac0d40266adf7eae5fd00df3db879","first_computed_at":"2026-05-18T02:55:36.546771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:36.546771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qxQus4ayB0W9HjXE1KgTNcWBe4APwRLcBPABTJUh6cqYtF5lvo0vfPtUvtmbp1bCmGPRtnfgeuajkbbNpA1PCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:36.547362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0844","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75534ca0bcc1cf75dd0b3e5e34e3c64373a04af87d3096b57e833d87bedce574","sha256:e0bca927d7bb689471020a1b80c1313474deeef8fec4bface37e45e84143a910"],"state_sha256":"da4b8cd39303563b5a6ecf0c63e32b884dc79e2190eef61c60efc4ebe80065f6"}