Strong clustering in type III entropic K-systems | Zendy

Fabio Benatti | Zendy; Heide Narnhofer | Zendy

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Strong clustering in type III entropic K-systems

Author(s) -

Fabio Benatti,

Heide Narnhofer

Publication year - 1997

Publication title -

monatshefte für mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 37

eISSN - 1436-5081

pISSN - 0026-9255

DOI - 10.1007/bf01319040

Subject(s) - von neumann entropy , subalgebra , mathematics , abelian group , von neumann architecture , quantum , pure mathematics , von neumann algebra , abelian von neumann algebra , entropy (arrow of time) , cluster analysis , mathematical physics , physics , quantum mechanics , algebra over a field , jordan algebra , quantum entanglement , algebra representation , statistics

It is shown that Complete Memory Loss (CML) formulated in terms of the Quantum Dynamical Entropy of Connes, Narnhofer and Thirring implies Strong Clustering for some typeIII von Neumann algebras including infinite quantum systems with quasi-free states. This generalizes analogous conclusions on Abelian and typeII1 von Neumann algebras. The result is based on the fact that optimal decompositions that obtain the so-called “Entropy of a Subalgebra” are under control in the two-dimensional case.

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