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Wada","submitted_at":"2001-10-02T02:01:53Z","abstract_excerpt":"For Tsallis' entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value $q^*$ of the entropic index such that the asymptotic rate $K_q \\equiv \\lim_{t \\to \\infty} \\{S_q(t)-S_q(0)\\} / t$ of increase in $S_q(t)$ remains finite whereas $K_q$ vanishes (diverges) for $q > q^* (q < q^*)$. We show that in spite of the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions, the pseudo-additive conditional entropy $S_q(t|0) \\equiv \\{S_q(t)-S_q(0)\\}/ \\{1+(1-q)S_q("},"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":"cond-mat/0110046","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2001-10-02T02:01:53Z","cross_cats_sorted":[],"title_canon_sha256":"24f5086296a87b83ec15df6a8b6f23f7b6757c737c8cbdc893e44495de15e1cc","abstract_canon_sha256":"888c775419842947e1d80c8e2801ba375497e699ebc7a89f2e882d140fe526ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:06.558176Z","signature_b64":"cXzAKcdqB6N06daY+pH/K48j/M0CV0qmsloRXwAk0g8KqGVhhE6PzoKFWvJRhgc4c7EUm+V/j1xsLTPldy70Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caaacbed91140ba0ccb62bb6e9b3e578206f44cddd9ebb22425434dd4e61c71e","last_reissued_at":"2026-05-18T01:40:06.557697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:06.557697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The additivity of the pseudo-additive conditional entropy for a proper Tsallis' entropic index","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"T. 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We show that in spite of the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions, the pseudo-additive conditional entropy $S_q(t|0) \\equiv \\{S_q(t)-S_q(0)\\}/ \\{1+(1-q)S_q("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0110046","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":"cond-mat/0110046","created_at":"2026-05-18T01:40:06.557761+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0110046v1","created_at":"2026-05-18T01:40:06.557761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0110046","created_at":"2026-05-18T01:40:06.557761+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKVMX3MRCQF2","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKVMX3MRCQF2BTFW","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKVMX3MR","created_at":"2026-05-18T12:25:50.845339+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/ZKVMX3MRCQF2BTFWFO3OTM7FPA","json":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA.json","graph_json":"https://pith.science/api/pith-number/ZKVMX3MRCQF2BTFWFO3OTM7FPA/graph.json","events_json":"https://pith.science/api/pith-number/ZKVMX3MRCQF2BTFWFO3OTM7FPA/events.json","paper":"https://pith.science/paper/ZKVMX3MR"},"agent_actions":{"view_html":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA","download_json":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA.json","view_paper":"https://pith.science/paper/ZKVMX3MR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0110046&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKVMX3MRCQF2BTFWFO3OTM7FPA/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKVMX3MRCQF2BTFWFO3OTM7FPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA/action/storage_attestation","attest_author":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA/action/author_attestation","sign_citation":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA/action/citation_signature","submit_replication":"https://pith.science/pith/ZKVMX3MRCQF2BTFWFO3OTM7FPA/action/replication_record"}},"created_at":"2026-05-18T01:40:06.557761+00:00","updated_at":"2026-05-18T01:40:06.557761+00:00"}