{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XIZAIXGMTO5EPCTOE5QDU2CH6H","short_pith_number":"pith:XIZAIXGM","schema_version":"1.0","canonical_sha256":"ba32045ccc9bba478a6e27603a6847f1ea03e7769d2561b94eb2219881916847","source":{"kind":"arxiv","id":"1101.2607","version":3},"attestation_state":"computed","paper":{"title":"Canonical equilibrium distribution derived from Helmholtz potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Gokhan Baris Bagci, Thomas Oikonomou, Ugur Tirnakli","submitted_at":"2011-01-13T16:33:42Z","abstract_excerpt":"Plastino and Curado [Phys. Rev. E 72, 047103 (2005)] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivatio"},"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":"1101.2607","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-01-13T16:33:42Z","cross_cats_sorted":[],"title_canon_sha256":"d3f4fba621aab284d4796ffd1d60f2ec91ce8d32ad7db38513f9f4eb118976aa","abstract_canon_sha256":"c27ce8a94d027ed114ef1df1c65ce405f40ac6374b117d4c7e4d8ef31ba472fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:40.366701Z","signature_b64":"m5GbsrKUxempXFTHiPkcrp3dzR3lKcNLvaAAQNKkCnskC9fJXbGYoNkYv7yijf8vzMPxA7J3JMIgwr5LuPPuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba32045ccc9bba478a6e27603a6847f1ea03e7769d2561b94eb2219881916847","last_reissued_at":"2026-05-18T02:03:40.365863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:40.365863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical equilibrium distribution derived from Helmholtz potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Gokhan Baris Bagci, Thomas Oikonomou, Ugur Tirnakli","submitted_at":"2011-01-13T16:33:42Z","abstract_excerpt":"Plastino and Curado [Phys. Rev. E 72, 047103 (2005)] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2607","kind":"arxiv","version":3},"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":"1101.2607","created_at":"2026-05-18T02:03:40.366015+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.2607v3","created_at":"2026-05-18T02:03:40.366015+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2607","created_at":"2026-05-18T02:03:40.366015+00:00"},{"alias_kind":"pith_short_12","alias_value":"XIZAIXGMTO5E","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XIZAIXGMTO5EPCTO","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XIZAIXGM","created_at":"2026-05-18T12:26:44.992195+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/XIZAIXGMTO5EPCTOE5QDU2CH6H","json":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H.json","graph_json":"https://pith.science/api/pith-number/XIZAIXGMTO5EPCTOE5QDU2CH6H/graph.json","events_json":"https://pith.science/api/pith-number/XIZAIXGMTO5EPCTOE5QDU2CH6H/events.json","paper":"https://pith.science/paper/XIZAIXGM"},"agent_actions":{"view_html":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H","download_json":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H.json","view_paper":"https://pith.science/paper/XIZAIXGM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.2607&json=true","fetch_graph":"https://pith.science/api/pith-number/XIZAIXGMTO5EPCTOE5QDU2CH6H/graph.json","fetch_events":"https://pith.science/api/pith-number/XIZAIXGMTO5EPCTOE5QDU2CH6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H/action/storage_attestation","attest_author":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H/action/author_attestation","sign_citation":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H/action/citation_signature","submit_replication":"https://pith.science/pith/XIZAIXGMTO5EPCTOE5QDU2CH6H/action/replication_record"}},"created_at":"2026-05-18T02:03:40.366015+00:00","updated_at":"2026-05-18T02:03:40.366015+00:00"}