An estimation of the logarithmic timescale in an ergodic dynamics

An estimation of the logarithmic timescale in quantum systems having an ergodic dynamics in the semiclassical limit of quasiclassical large parameters, is presented. The estimation is based on the existence of finite generators for ergodic measure-preserving transformations having a finite Kolmogorov–Sinai (KS) entropy and on the time rescaling property of the KS-entropy. The results are in agreement with the obtained in the literature but with a simpler mathematics and within the context of the ergodic theory.