{"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 $\\IM$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701186","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"}