Dynamical entropy of quasi-local algebras in quantum statistical mechanics
type: Item
instance of: scholarly article
title: Dynamical entropy of quasi-local algebras in quantum statistical mechanics
zbMATH Open document ID: 0764.46056
DOI: 10.1007/BF02099194
author: Yong Moon Park
author: Hyun Hye Shin
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: The notion of the dynamical entropy of automorphisms of \(C^*\)-algebras was defined by \textit{A. Connes}, \textit{H. Narnhofer} and \textit{W. Thirring} [Commun. Math. Phys. 112, 691-719 (1987; Zbl 0637.46073)], who also proved a Kolmogorov-Sinai type theorem in the case when the algebra is approximately finite. In the paper under review, the results are extended to quasi-local algebras with a locally normal state (i.e. a state which is normal when restricted to any of the local algebras). The quasi-local algebra is assumed to satisfy the tensor product property. As an application, the dynamical entropy of space translations for product states of the unbounded quantum lattice system is computed.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 54739
zbMATH Keywords: dynamical entropy of automorphisms of \(C^*\)-algebras
zbMATH Keywords: Kolmogorov-Sinai type theorem
zbMATH Keywords: approximately finite
zbMATH Keywords: quasi-local algebras with a locally normal state
zbMATH Keywords: tensor product property
zbMATH Keywords: dynamical entropy of space translations for product states
zbMATH Keywords: unbounded quantum lattice system
reviewed by: Stanisław Goldstein
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02099194
OpenAlex ID: W1983498848
description: scientific article; zbMATH DE number 54739