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The function $f[A(t)]$ is supposed to be an operator acting on the same space as the operator $A(t)$. We use the basis which diagonalizes A(t), i.e., $A_{i j}=\\lambda_i \\delta_{i j}$, and obtain $[\\frac{\\partial f[A(t)]}{\\partial t}]_{i j}=[\\frac{\\partial A}{\\partial t}]_ {i j}\\frac{f(\\lambda_j) - f(\\lambda_i)} {\\lambda_j - \\lambda_i}$. In addition to this, we show that further","authors_text":"Argentina), Astronomia y Fisica, Brazil), Ciudad Universitaria, Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Cordoba, Domingo Prato (Facultad de Matematica, Rio de Janeiro-RJ, Universidad Nacional de Cordoba","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-06-11T16:55:11Z","title":"Functions of linear operators: Parameter differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9906173","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:49d6369a59c27db0f5a56348cbafae6d17b9062f2b1f9be5c0ea28f7bbe01e9f","target":"record","created_at":"2026-05-18T01:39:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4208fcbe84a186dd97c0a5df12a13a4df8f0a5b7a1a82b292f5fec092300912b","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-06-11T16:55:11Z","title_canon_sha256":"ccfb664f45af2800e107518387ce266ebadddcf574e37a79bdcb25527905b5f3"},"schema_version":"1.0","source":{"id":"cond-mat/9906173","kind":"arxiv","version":1}},"canonical_sha256":"511a6736fcd06cc488d5b52599c96945bf6fba174dd61178d5a7919375675aa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"511a6736fcd06cc488d5b52599c96945bf6fba174dd61178d5a7919375675aa8","first_computed_at":"2026-05-18T01:39:28.702433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:28.702433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9SmnsHYMOk/wgOlESRZNfgijjZgZWLKfKo6CQ4QltAcVGzUN6z83k7L2hW6d4w+XS7f6qQ8aWY7tAIoob4Z9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:28.703090Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9906173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49d6369a59c27db0f5a56348cbafae6d17b9062f2b1f9be5c0ea28f7bbe01e9f","sha256:8568f17e39cad6a3a4c147836bf42cc907a3a36990bf2ab597f437e178aee51c"],"state_sha256":"265bb7d6e18281a57e3b6b3d1f336fc59c90b5c59657d9c62f0e9463bbdbb04a"}