Quantum Mechanical Tools in Applications to Classical Dynamical Systems

Abstract

A recently developed approach to classical and quantum dynamical entropy involving generalized partitions of unity allows one to use the mathematical formalism typical for quantum statistical mechanics to analyze classical dynamical systems. In particular, density matrices, their von Neumann entropy, and irreversible quantum dynamical maps corresponding to measurement processes appear. To illustrate the power of this new technique we give a simple proof of the Ruelle's inequality between the Kolmogorov-Sinai entropy and the Lyapunov exponents. Continuous time classical dynamical systems are briefly discussed also.