Logical entropy of quantum dynamical systems

Abstract

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.

Keywords

• logical entropy
• quantum logic
• dynamical system
• partition
• 02.10.ab
• 02.30.cj
• 89.70.cf