{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:A5N24QV2BK4PLYKZJCLLMLQF7H","short_pith_number":"pith:A5N24QV2","schema_version":"1.0","canonical_sha256":"075bae42ba0ab8f5e1594896b62e05f9d463a9fa83f45b7459723eedd8dc466f","source":{"kind":"arxiv","id":"1406.2733","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Constantino Tsallis, Daniel G. Barci, Zochil Gonz\\'alez Arenas","submitted_at":"2014-06-10T22:12:04Z","abstract_excerpt":"We deduce a nonlinear and inhomogeneous Fokker-Planck equation within a generalized Stratonovich, or stochastic $\\alpha$-, prescription ($\\alpha=0$, $1/2$ and $1$ respectively correspond to the It\\^o, Stratonovich and anti-It\\^o prescriptions). We obtain its stationary state $p_{st}(x)$ for a class of constitutive relations between drift and diffusion and show that it has a $q$-exponential form, $p_{st}(x) = N_q[1 - (1-q)\\beta V(x)]^{1/(1-q)}$, with an index $q$ which does not depend on $\\alpha$ in the presence of any nonvanishing nonlinearity. This is in contrast with the linear case, for whi"},"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":"1406.2733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-10T22:12:04Z","cross_cats_sorted":[],"title_canon_sha256":"5e045a108af35c992addffee80d7c55176909456bc43fdad009b52484b57d4f3","abstract_canon_sha256":"e40639f2c9aaed56605b0a93d010e5bba2309d00aa6ca5a22923240d6f675507"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:07.757456Z","signature_b64":"nRJCyn2hsvMY5vemoFzpov46B2IJx004Co8rdIgbJa7X80KEQ02jDTn8ty0jTgEiGRM4xgGs6XN3BjRJFTExAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"075bae42ba0ab8f5e1594896b62e05f9d463a9fa83f45b7459723eedd8dc466f","last_reissued_at":"2026-05-18T02:42:07.757055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:07.757055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Constantino Tsallis, Daniel G. Barci, Zochil Gonz\\'alez Arenas","submitted_at":"2014-06-10T22:12:04Z","abstract_excerpt":"We deduce a nonlinear and inhomogeneous Fokker-Planck equation within a generalized Stratonovich, or stochastic $\\alpha$-, prescription ($\\alpha=0$, $1/2$ and $1$ respectively correspond to the It\\^o, Stratonovich and anti-It\\^o prescriptions). We obtain its stationary state $p_{st}(x)$ for a class of constitutive relations between drift and diffusion and show that it has a $q$-exponential form, $p_{st}(x) = N_q[1 - (1-q)\\beta V(x)]^{1/(1-q)}$, with an index $q$ which does not depend on $\\alpha$ in the presence of any nonvanishing nonlinearity. This is in contrast with the linear case, for whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2733","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":"1406.2733","created_at":"2026-05-18T02:42:07.757105+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.2733v1","created_at":"2026-05-18T02:42:07.757105+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2733","created_at":"2026-05-18T02:42:07.757105+00:00"},{"alias_kind":"pith_short_12","alias_value":"A5N24QV2BK4P","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"A5N24QV2BK4PLYKZ","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"A5N24QV2","created_at":"2026-05-18T12:28:19.803747+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/A5N24QV2BK4PLYKZJCLLMLQF7H","json":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H.json","graph_json":"https://pith.science/api/pith-number/A5N24QV2BK4PLYKZJCLLMLQF7H/graph.json","events_json":"https://pith.science/api/pith-number/A5N24QV2BK4PLYKZJCLLMLQF7H/events.json","paper":"https://pith.science/paper/A5N24QV2"},"agent_actions":{"view_html":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H","download_json":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H.json","view_paper":"https://pith.science/paper/A5N24QV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.2733&json=true","fetch_graph":"https://pith.science/api/pith-number/A5N24QV2BK4PLYKZJCLLMLQF7H/graph.json","fetch_events":"https://pith.science/api/pith-number/A5N24QV2BK4PLYKZJCLLMLQF7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H/action/storage_attestation","attest_author":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H/action/author_attestation","sign_citation":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H/action/citation_signature","submit_replication":"https://pith.science/pith/A5N24QV2BK4PLYKZJCLLMLQF7H/action/replication_record"}},"created_at":"2026-05-18T02:42:07.757105+00:00","updated_at":"2026-05-18T02:42:07.757105+00:00"}