{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7OYRJZ7DEW5GGOPCPBGIZC5B7C","short_pith_number":"pith:7OYRJZ7D","schema_version":"1.0","canonical_sha256":"fbb114e7e325ba6339e2784c8c8ba1f882dac0d40266adf7eae5fd00df3db879","source":{"kind":"arxiv","id":"1212.0844","version":5},"attestation_state":"computed","paper":{"title":"Duration of local violations of the second law of thermodynamics along single trajectories in phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel Dom\\'inguez, Reinaldo Garc\\'ia-Garc\\'ia","submitted_at":"2012-12-04T20:12:36Z","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 "},"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":"1212.0844","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-04T20:12:36Z","cross_cats_sorted":[],"title_canon_sha256":"93f6d27187c011a0017b2e704c94a5a1f3a5b7bdd8e8a4b9fef83b34a30e0b76","abstract_canon_sha256":"da6a04979ee6e7a770221ba73b2bb22e58ee15b69beee503f149b2a5d26d6dae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:36.547362Z","signature_b64":"qxQus4ayB0W9HjXE1KgTNcWBe4APwRLcBPABTJUh6cqYtF5lvo0vfPtUvtmbp1bCmGPRtnfgeuajkbbNpA1PCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbb114e7e325ba6339e2784c8c8ba1f882dac0d40266adf7eae5fd00df3db879","last_reissued_at":"2026-05-18T02:55:36.546771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:36.546771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Duration of local violations of the second law of thermodynamics along single trajectories in phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel Dom\\'inguez, Reinaldo Garc\\'ia-Garc\\'ia","submitted_at":"2012-12-04T20:12:36Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0844","kind":"arxiv","version":5},"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":"1212.0844","created_at":"2026-05-18T02:55:36.546857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0844v5","created_at":"2026-05-18T02:55:36.546857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0844","created_at":"2026-05-18T02:55:36.546857+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OYRJZ7DEW5G","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OYRJZ7DEW5GGOPC","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OYRJZ7D","created_at":"2026-05-18T12:26:58.693483+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/7OYRJZ7DEW5GGOPCPBGIZC5B7C","json":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C.json","graph_json":"https://pith.science/api/pith-number/7OYRJZ7DEW5GGOPCPBGIZC5B7C/graph.json","events_json":"https://pith.science/api/pith-number/7OYRJZ7DEW5GGOPCPBGIZC5B7C/events.json","paper":"https://pith.science/paper/7OYRJZ7D"},"agent_actions":{"view_html":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C","download_json":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C.json","view_paper":"https://pith.science/paper/7OYRJZ7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0844&json=true","fetch_graph":"https://pith.science/api/pith-number/7OYRJZ7DEW5GGOPCPBGIZC5B7C/graph.json","fetch_events":"https://pith.science/api/pith-number/7OYRJZ7DEW5GGOPCPBGIZC5B7C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C/action/storage_attestation","attest_author":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C/action/author_attestation","sign_citation":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C/action/citation_signature","submit_replication":"https://pith.science/pith/7OYRJZ7DEW5GGOPCPBGIZC5B7C/action/replication_record"}},"created_at":"2026-05-18T02:55:36.546857+00:00","updated_at":"2026-05-18T02:55:36.546857+00:00"}