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In a recent paper, we have proved that the mean entropy $s(\\omega)$ is a complete invariant for certain classes of translation invariant state $\\omega$ of $\\IM$. In this paper, we have developed a general theory for dynamical entropy for an automorphism on an arbitrary $C^*$- or von-Neumann algebras based on repeated admissible measurement proce"},"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":"math/0701186","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2007-01-06T10:20:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f1a8d681fd3a89c98c082f64723f0a66ea3f712f1efef187d47782c5b5c68985","abstract_canon_sha256":"fd1df1be9ec8de33822cc4d6ecd59bd67bc8b1e0627e512dc5b7ff8e60b7952f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:05.076115Z","signature_b64":"fdlIJFlm58G52OwksrNXF0L3pL/oT0tI33u/qtb+OrpEC5W9glXdqULi/FfyZINDDR5BCRYlT/+fmW8zGsVXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3646634780563bd34210120adad5bd1820ef5f89ae411578745db7280792c7d","last_reissued_at":"2026-05-18T00:27:05.075585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:05.075585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Translation invariant state and its mean entropy-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Anilesh Mohari","submitted_at":"2007-01-06T10:20:45Z","abstract_excerpt":"Let $\\IM =\\otimes_{n \\in \\IZ}\\!M^{(n)}(\\IC)$ be the two sided infinite tensor product $C^*$-algebra of $d$ dimensional matrices $\\!M^{(n)}(\\IC)=\\!M_d(\\IC)$ over the field of complex numbers $\\IC$. Let $\\omega$ be a translation invariant state of $\\IM$. In a recent paper, we have proved that the mean entropy $s(\\omega)$ is a complete invariant for certain classes of translation invariant state $\\omega$ of $\\IM$. 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