{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ILJNYDIGGKTWBX7QOADGYVOPDR","short_pith_number":"pith:ILJNYDIG","schema_version":"1.0","canonical_sha256":"42d2dc0d0632a760dff070066c55cf1c4910817faa06c0c23ebcf60d2198e289","source":{"kind":"arxiv","id":"1206.5888","version":1},"attestation_state":"computed","paper":{"title":"Microcanonical Origin of the Maximum Entropy Principle for Open Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Julian Lee","submitted_at":"2012-06-26T06:07:59Z","abstract_excerpt":"The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe consisting of the open system and the heat bath, by taking the limit where the heat bath is much larger than the system of interest. Alternatively, the Boltzmann distribution can be derived from the Maximum Entropy Principle, where the Gibbs-Shannon entropy is maximized under the constraint that the mean energy of the open system is fixed. To ma"},"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":"1206.5888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-26T06:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"f62b3c4e22f914448c998624e60a7b6a1176ff198a4e4a12a801a3c929502678","abstract_canon_sha256":"6fd52ff2367f9aa7f88ce3a837ed7a198bd3cc29c39322770ad95a680ff9953e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:41.808433Z","signature_b64":"0Q5fWAixc3GspVv4jW/JGyGgLCSqE72xsTNk1kwkQm7yqAxBEK1/j3/w1rYUMSo33T7YOSPBG0qOGE68u+t4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42d2dc0d0632a760dff070066c55cf1c4910817faa06c0c23ebcf60d2198e289","last_reissued_at":"2026-05-18T01:56:41.808021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:41.808021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Microcanonical Origin of the Maximum Entropy Principle for Open Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Julian Lee","submitted_at":"2012-06-26T06:07:59Z","abstract_excerpt":"The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe consisting of the open system and the heat bath, by taking the limit where the heat bath is much larger than the system of interest. Alternatively, the Boltzmann distribution can be derived from the Maximum Entropy Principle, where the Gibbs-Shannon entropy is maximized under the constraint that the mean energy of the open system is fixed. To ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5888","kind":"arxiv","version":1},"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":"1206.5888","created_at":"2026-05-18T01:56:41.808084+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.5888v1","created_at":"2026-05-18T01:56:41.808084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5888","created_at":"2026-05-18T01:56:41.808084+00:00"},{"alias_kind":"pith_short_12","alias_value":"ILJNYDIGGKTW","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"ILJNYDIGGKTWBX7Q","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"ILJNYDIG","created_at":"2026-05-18T12:27:09.501522+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/ILJNYDIGGKTWBX7QOADGYVOPDR","json":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR.json","graph_json":"https://pith.science/api/pith-number/ILJNYDIGGKTWBX7QOADGYVOPDR/graph.json","events_json":"https://pith.science/api/pith-number/ILJNYDIGGKTWBX7QOADGYVOPDR/events.json","paper":"https://pith.science/paper/ILJNYDIG"},"agent_actions":{"view_html":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR","download_json":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR.json","view_paper":"https://pith.science/paper/ILJNYDIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.5888&json=true","fetch_graph":"https://pith.science/api/pith-number/ILJNYDIGGKTWBX7QOADGYVOPDR/graph.json","fetch_events":"https://pith.science/api/pith-number/ILJNYDIGGKTWBX7QOADGYVOPDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR/action/storage_attestation","attest_author":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR/action/author_attestation","sign_citation":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR/action/citation_signature","submit_replication":"https://pith.science/pith/ILJNYDIGGKTWBX7QOADGYVOPDR/action/replication_record"}},"created_at":"2026-05-18T01:56:41.808084+00:00","updated_at":"2026-05-18T01:56:41.808084+00:00"}