On the Relation of KS Entropy and Permutation Entropy

TL;DR

This paper explores the relationship between Kolmogorov-Sinai entropy and permutation entropy in time-discrete dynamical systems, building on recent ordinal characterizations to deepen understanding of their connection.

Contribution

It provides a discussion on how permutation entropy relates to Kolmogorov-Sinai entropy using a recent ordinal characterization, extending prior results.

Findings

Permutation entropy and Kolmogorov-Sinai entropy coincide for certain systems.

The paper offers insights into the ordinal-based relationship between these entropies.

It advances the theoretical understanding of entropy measures in dynamical systems.

Abstract

Since Bandt et al. have shown that the permutation entropy and the Kolmogorov-Sinai entropy coincide for piecewise monotone interval maps, the relationship of both entropies for time-discrete dynamical systems is of a certain interest. The aim of this paper is a discussion of this relationship on the basis of an ordinal characterization of the Kolmogorov-Sinai entropy recently given.