{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:T3RN37D6VWFF74LH36WA3QUBVQ","short_pith_number":"pith:T3RN37D6","schema_version":"1.0","canonical_sha256":"9ee2ddfc7ead8a5ff167dfac0dc281ac1c89bb4130af625d7059ec8b28345702","source":{"kind":"arxiv","id":"1402.3380","version":2},"attestation_state":"computed","paper":{"title":"The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hal Tasaki, Sheldon Goldstein, Takashi Hara","submitted_at":"2014-02-14T06:41:27Z","abstract_excerpt":"We study the problem of the approach to equilibrium in a macroscopic quantum system in an abstract setting. We prove that, for a typical choice of \"nonequilibrium subspace\", any initial state (from the energy shell) thermalizes, and in fact does so very quickly, on the order of the Boltzmann time $\\tau__\\mathrm{B}:=h/(k_\\mathrm{B}T)$. This apparently unrealistic, but mathematically rigorous, conclusion has the important physical implication that the moderately slow decay observed in reality is not typical in the present setting.\n  The fact that macroscopic systems approach thermal equilibrium "},"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":"1402.3380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-02-14T06:41:27Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"34fc1ccfb218bc5ff7927c05e59f7ca727bf877874449ea87edad0d6e5b053ab","abstract_canon_sha256":"15339a17d18498a37e15fc1d06a91646505e5530f520298d7e399606affa1ccd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:48.372250Z","signature_b64":"LM/vYWDurGVvQts7T8GPL0HyNhb7Ikg+uCs2FUPoTGKXqIOB10p/PffolBRW7I1azs9oSH6bB/RaEAeGCQ8ZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee2ddfc7ead8a5ff167dfac0dc281ac1c89bb4130af625d7059ec8b28345702","last_reissued_at":"2026-05-18T02:51:48.371714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:48.371714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hal Tasaki, Sheldon Goldstein, Takashi Hara","submitted_at":"2014-02-14T06:41:27Z","abstract_excerpt":"We study the problem of the approach to equilibrium in a macroscopic quantum system in an abstract setting. We prove that, for a typical choice of \"nonequilibrium subspace\", any initial state (from the energy shell) thermalizes, and in fact does so very quickly, on the order of the Boltzmann time $\\tau__\\mathrm{B}:=h/(k_\\mathrm{B}T)$. This apparently unrealistic, but mathematically rigorous, conclusion has the important physical implication that the moderately slow decay observed in reality is not typical in the present setting.\n  The fact that macroscopic systems approach thermal equilibrium "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3380","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":"1402.3380","created_at":"2026-05-18T02:51:48.371822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3380v2","created_at":"2026-05-18T02:51:48.371822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3380","created_at":"2026-05-18T02:51:48.371822+00:00"},{"alias_kind":"pith_short_12","alias_value":"T3RN37D6VWFF","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"T3RN37D6VWFF74LH","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"T3RN37D6","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2310.18880","citing_title":"Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ","json":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ.json","graph_json":"https://pith.science/api/pith-number/T3RN37D6VWFF74LH36WA3QUBVQ/graph.json","events_json":"https://pith.science/api/pith-number/T3RN37D6VWFF74LH36WA3QUBVQ/events.json","paper":"https://pith.science/paper/T3RN37D6"},"agent_actions":{"view_html":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ","download_json":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ.json","view_paper":"https://pith.science/paper/T3RN37D6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3380&json=true","fetch_graph":"https://pith.science/api/pith-number/T3RN37D6VWFF74LH36WA3QUBVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/T3RN37D6VWFF74LH36WA3QUBVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ/action/storage_attestation","attest_author":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ/action/author_attestation","sign_citation":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ/action/citation_signature","submit_replication":"https://pith.science/pith/T3RN37D6VWFF74LH36WA3QUBVQ/action/replication_record"}},"created_at":"2026-05-18T02:51:48.371822+00:00","updated_at":"2026-05-18T02:51:48.371822+00:00"}