Non-Bernoullian Quantum K-Systems

Abstract:

We construct an uncountable family of pairwise non-conjugate non-Bernoullian K-systems of type III ₁ with the same finite CNT-entropy. We also investigate clustering properties of multiple channel entropies for strong asymptotically abelian systems of type II and III. We prove that a wide enough class of systems has the K-property. In particular, such systems as the space translations of a one-dimensional quantum lattice with the Gibbs states of Araki, the space translations of the CCR-algebra and the even part of the CAR-algebra with the quasi-free states of Park and Shin, non-commutative Markov shifts in the Accardi sense are entropic K-systems.

Dedicated to Professor Walter Thirring on his 70th birthday.