{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LYTV2MGRTHHDYJXUG7UPBECJUS","short_pith_number":"pith:LYTV2MGR","schema_version":"1.0","canonical_sha256":"5e275d30d199ce3c26f437e8f09049a4aad785b025c5c1f287f0b774222d2b42","source":{"kind":"arxiv","id":"1212.6767","version":6},"attestation_state":"computed","paper":{"title":"General H-theorem and entropies that violate the second law","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexander N. Gorban","submitted_at":"2012-12-30T19:37:08Z","abstract_excerpt":"$H$-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma). Originally, the $H$-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy). Many new entropies and divergences have been proposed during last decades and for all of them the $H$-theorem is needed. This note "},"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":"1212.6767","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-12-30T19:37:08Z","cross_cats_sorted":[],"title_canon_sha256":"aaaefc93b32530a6fdc45c83c872f5aa4b6c8aa6230ccd4ba384f5bb88f8978f","abstract_canon_sha256":"a0c781b769f3bc2218c408ee54357845448280ee473d5f480da2dd7f779e6387"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:47.631370Z","signature_b64":"savcr9QzedM8zM7Re0Nai+rwNA5GKyQcli0E7N25mAp/9PjnOyuQKosePxc3pCvNka37vR+ZRv1yIkhluNvrDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e275d30d199ce3c26f437e8f09049a4aad785b025c5c1f287f0b774222d2b42","last_reissued_at":"2026-05-18T02:40:47.630857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:47.630857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General H-theorem and entropies that violate the second law","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexander N. Gorban","submitted_at":"2012-12-30T19:37:08Z","abstract_excerpt":"$H$-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the information processing lemma). Originally, the $H$-theorem and the information processing lemma were proved for the classical Boltzmann-Gibbs-Shannon entropy and for the correspondent divergence (the relative entropy). Many new entropies and divergences have been proposed during last decades and for all of them the $H$-theorem is needed. This note "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6767","kind":"arxiv","version":6},"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":"1212.6767","created_at":"2026-05-18T02:40:47.630941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6767v6","created_at":"2026-05-18T02:40:47.630941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6767","created_at":"2026-05-18T02:40:47.630941+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYTV2MGRTHHD","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYTV2MGRTHHDYJXU","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYTV2MGR","created_at":"2026-05-18T12:27:14.488303+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/LYTV2MGRTHHDYJXUG7UPBECJUS","json":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS.json","graph_json":"https://pith.science/api/pith-number/LYTV2MGRTHHDYJXUG7UPBECJUS/graph.json","events_json":"https://pith.science/api/pith-number/LYTV2MGRTHHDYJXUG7UPBECJUS/events.json","paper":"https://pith.science/paper/LYTV2MGR"},"agent_actions":{"view_html":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS","download_json":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS.json","view_paper":"https://pith.science/paper/LYTV2MGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6767&json=true","fetch_graph":"https://pith.science/api/pith-number/LYTV2MGRTHHDYJXUG7UPBECJUS/graph.json","fetch_events":"https://pith.science/api/pith-number/LYTV2MGRTHHDYJXUG7UPBECJUS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS/action/storage_attestation","attest_author":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS/action/author_attestation","sign_citation":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS/action/citation_signature","submit_replication":"https://pith.science/pith/LYTV2MGRTHHDYJXUG7UPBECJUS/action/replication_record"}},"created_at":"2026-05-18T02:40:47.630941+00:00","updated_at":"2026-05-18T02:40:47.630941+00:00"}