Quantum Kolmogorov-Sinai entropy and Pesin relation

TL;DR

This paper introduces a quantum version of Kolmogorov-Sinai entropy derived from entropy production due to weak coupling with an auxiliary bath, establishing a quantum Pesin relation in the semiclassical limit.

Contribution

It defines a fully quantum entropy measure linked to phase-space expansion and demonstrates its reduction to classical entropy in the semiclassical limit.

Findings

Quantum entropy reduces to classical in semiclassical limit

Established a quantum Pesin relation between entropy and phase-space expansion

Generalized to cases with sublinear entropy growth

Abstract

We discuss a quantum Kolmogorov-Sinai entropy defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath. The expressions we obtain are fully quantum, but require that the system is such that there is a separation between the Ehrenfest and the correlation timescales. We show that they reduce to the classical definition in the semiclassical limit, one instance where this separation holds. We show a quantum (Pesin) relation between this entropy and the sum of positive eigenvalues of a matrix describing phase-space expansion. Generalizations to the case where entropy grows sublinearly with time are possible.