Dynamical entropy of quasi-local algebras in quantum statistical mechanics
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.
dynamical entropy of automorphisms of \(C^*\)-algebras
quasi-local algebras with a locally normal state
dynamical entropy of space translations for product states
scientific article; zbMATH DE number 54739
scientific article