{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SWYED5SRWN7RANEOLCV4A4NTLJ","short_pith_number":"pith:SWYED5SR","schema_version":"1.0","canonical_sha256":"95b041f651b37f10348e58abc071b35a5a2b6bbe3ddd89a0a3afdd3920351da3","source":{"kind":"arxiv","id":"1608.00223","version":2},"attestation_state":"computed","paper":{"title":"Entropy production inequalities for the Kac Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Amit Einav, Eric A. Carlen, Maria C. Carvalho","submitted_at":"2016-07-31T14:44:26Z","abstract_excerpt":"Mark Kac introduced what is now called 'the Kac Walk' with the aim of investigating the spatially homogeneous Boltzmann equation by probabilistic means. Much recent work, discussed below, on Kac's program has run in the other direction: using recent results on the Boltzmann equation, or its one-dimensional analog, the non-linear Kac-Boltzmann equation, to prove results for the Kac Walk. Here we investigate new functional inequalities for the Kac Walk pertaining to entropy production, and introduce a new form of `chaoticity'. We then show how these entropy production inequalities imply entropy "},"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":"1608.00223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-31T14:44:26Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"2ec26172679e05ac4ed8c8f4c8aded30428f95040bf69501ab53acad4ad1f112","abstract_canon_sha256":"c62a555bf4d4e7b98950665ddf2da3a6fb2f3048733e0d2f0fb5cc46fbd95624"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:20.854133Z","signature_b64":"0CXkDYzx8zT2bcjvm82KEE1WU9O89wd7Dn8W+LAJL/Zq96RJHIgcUq95LcMFKOzMIBSJtSLVm1JhWOQ42h2tDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b041f651b37f10348e58abc071b35a5a2b6bbe3ddd89a0a3afdd3920351da3","last_reissued_at":"2026-05-18T00:46:20.853772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:20.853772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy production inequalities for the Kac Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Amit Einav, Eric A. Carlen, Maria C. Carvalho","submitted_at":"2016-07-31T14:44:26Z","abstract_excerpt":"Mark Kac introduced what is now called 'the Kac Walk' with the aim of investigating the spatially homogeneous Boltzmann equation by probabilistic means. Much recent work, discussed below, on Kac's program has run in the other direction: using recent results on the Boltzmann equation, or its one-dimensional analog, the non-linear Kac-Boltzmann equation, to prove results for the Kac Walk. Here we investigate new functional inequalities for the Kac Walk pertaining to entropy production, and introduce a new form of `chaoticity'. We then show how these entropy production inequalities imply entropy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00223","kind":"arxiv","version":2},"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":"1608.00223","created_at":"2026-05-18T00:46:20.853825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.00223v2","created_at":"2026-05-18T00:46:20.853825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00223","created_at":"2026-05-18T00:46:20.853825+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWYED5SRWN7R","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWYED5SRWN7RANEO","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWYED5SR","created_at":"2026-05-18T12:30:44.179134+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/SWYED5SRWN7RANEOLCV4A4NTLJ","json":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ.json","graph_json":"https://pith.science/api/pith-number/SWYED5SRWN7RANEOLCV4A4NTLJ/graph.json","events_json":"https://pith.science/api/pith-number/SWYED5SRWN7RANEOLCV4A4NTLJ/events.json","paper":"https://pith.science/paper/SWYED5SR"},"agent_actions":{"view_html":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ","download_json":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ.json","view_paper":"https://pith.science/paper/SWYED5SR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.00223&json=true","fetch_graph":"https://pith.science/api/pith-number/SWYED5SRWN7RANEOLCV4A4NTLJ/graph.json","fetch_events":"https://pith.science/api/pith-number/SWYED5SRWN7RANEOLCV4A4NTLJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ/action/storage_attestation","attest_author":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ/action/author_attestation","sign_citation":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ/action/citation_signature","submit_replication":"https://pith.science/pith/SWYED5SRWN7RANEOLCV4A4NTLJ/action/replication_record"}},"created_at":"2026-05-18T00:46:20.853825+00:00","updated_at":"2026-05-18T00:46:20.853825+00:00"}