Quantum Kolmogorov-Sinai entropy and Pesin relation

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 expression we obtain is fully quantum, but requires that the system is such that there is a separation between the Ehrenfest and the correlation timescales. We show that it reduces 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.