{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7NYG4HPAIJ5EEXJSC54PFRWFYD","short_pith_number":"pith:7NYG4HPA","schema_version":"1.0","canonical_sha256":"fb706e1de0427a425d321778f2c6c5c0cc2f2ba26a1d2b4c99ac54895a17b67d","source":{"kind":"arxiv","id":"1811.00646","version":2},"attestation_state":"computed","paper":{"title":"The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Jean-Bernard Bru, Laerte Sodr\\'e, Leandro Beraldo e Silva, Monica Valluri, Walter de Siqueira Pedra","submitted_at":"2018-11-01T21:58:39Z","abstract_excerpt":"We investigate the old problem of the fast relaxation of collisionless $N$-body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreteness effects. We integrate orbit ensembles in fixed external potentials, estimating the entropy of the ensemble to analyze the time evolution of the distribution function. We show that these estimates capture the correct physical behavior expected from the 2nd Law of Thermodynamics, without any spurious entropy production. For self-consistent (i.e. stationary) samples, the entropy is conserved, while for non-self-cons"},"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":"1811.00646","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2018-11-01T21:58:39Z","cross_cats_sorted":[],"title_canon_sha256":"51c17e697ae62769beb731326e5cfdece40cc49a6e8a88ef961b577b92631ec9","abstract_canon_sha256":"7b2999cf49ff88571b6b67a783616932eb0b26a2cfbd85d3548bdfdf1280faf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:19.280917Z","signature_b64":"3DWvJZCDKEdSPycbTBqi/DGbQ+ADnRq6T+kgqz6Qb6LAVBspvQ4+lTkiueBudecegzf8r01LfwwKGXBnJxKoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb706e1de0427a425d321778f2c6c5c0cc2f2ba26a1d2b4c99ac54895a17b67d","last_reissued_at":"2026-05-17T23:55:19.280539Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:19.280539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The discreteness-driven relaxation of collisionless gravitating systems: entropy evolution in external potentials, N-dependence and the role of chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Jean-Bernard Bru, Laerte Sodr\\'e, Leandro Beraldo e Silva, Monica Valluri, Walter de Siqueira Pedra","submitted_at":"2018-11-01T21:58:39Z","abstract_excerpt":"We investigate the old problem of the fast relaxation of collisionless $N$-body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreteness effects. We integrate orbit ensembles in fixed external potentials, estimating the entropy of the ensemble to analyze the time evolution of the distribution function. We show that these estimates capture the correct physical behavior expected from the 2nd Law of Thermodynamics, without any spurious entropy production. For self-consistent (i.e. stationary) samples, the entropy is conserved, while for non-self-cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00646","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":"1811.00646","created_at":"2026-05-17T23:55:19.280599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.00646v2","created_at":"2026-05-17T23:55:19.280599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00646","created_at":"2026-05-17T23:55:19.280599+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NYG4HPAIJ5E","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NYG4HPAIJ5EEXJS","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NYG4HPA","created_at":"2026-05-18T12:32:11.075285+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/7NYG4HPAIJ5EEXJSC54PFRWFYD","json":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD.json","graph_json":"https://pith.science/api/pith-number/7NYG4HPAIJ5EEXJSC54PFRWFYD/graph.json","events_json":"https://pith.science/api/pith-number/7NYG4HPAIJ5EEXJSC54PFRWFYD/events.json","paper":"https://pith.science/paper/7NYG4HPA"},"agent_actions":{"view_html":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD","download_json":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD.json","view_paper":"https://pith.science/paper/7NYG4HPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.00646&json=true","fetch_graph":"https://pith.science/api/pith-number/7NYG4HPAIJ5EEXJSC54PFRWFYD/graph.json","fetch_events":"https://pith.science/api/pith-number/7NYG4HPAIJ5EEXJSC54PFRWFYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD/action/storage_attestation","attest_author":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD/action/author_attestation","sign_citation":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD/action/citation_signature","submit_replication":"https://pith.science/pith/7NYG4HPAIJ5EEXJSC54PFRWFYD/action/replication_record"}},"created_at":"2026-05-17T23:55:19.280599+00:00","updated_at":"2026-05-17T23:55:19.280599+00:00"}