2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91346Two non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in the quantisation parameter. The model of the quantised hyperbolic automorphisms of the 2-torus is examined in detail.LaTeX, 41 pages; v2: small changes and corrected typosQuantum PhysicsMathematical Physicstext