Logical entropy of quantum dynamical systems

This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.

Spectrum of quantum dynamical systems: Subsystems and entropy

In the present paper, we have studied quantum dynamical systems of difference posets, their equivalence, subsystems and spectra. It is shown that every subsystem of a mixing quantum dynamical system is mixing, and also a bounded spectrum of quantum dynamical systems has its supremum, and all such suprema are equivalent. Entropy of subsystems of a quantum dynamical system of orthomodular lattices is also investigated.