# An estimation of the logarithmic timescale in an ergodic dynamics

## TL;DR

This paper estimates the logarithmic timescale in ergodic quantum systems using ergodic theory and KS-entropy, providing a simpler mathematical approach that aligns with existing literature.

## Contribution

It introduces a novel estimation method for the logarithmic timescale in ergodic quantum systems based on finite generators and KS-entropy properties.

## Key findings

- Estimation aligns with previous results in the literature.
- Uses ergodic theory to simplify the mathematical framework.
- Provides a new perspective on timescale estimation in quantum ergodic systems.

## Abstract

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.