Infinite dimensional analysis quantum probability and related topics vol:2 issue:4 pages:511-527
In this paper, we are mainly concerned with the computation of the dynamical entropy for the noncommutative toral automorphisms and the noncommutative shifts on a spin chain. The entropy that we consider is based on coarse-grained models of the system. In contrast to the classical situation, successive observations of a quantum system can generate entropy by themselves. We pay special attention to the delicate problem of delimiting a natural class of models for computing the entropy.