Entropy determination based on the ordinal structure of a dynamical system

TL;DR

This paper reviews and extends methods for estimating the Kolmogorov-Sinai entropy of measure-preserving dynamical systems using ordinal partitions, emphasizing minimal measurement requirements for accurate entropy estimation.

Contribution

It generalizes the theory of entropy determination via ordinal structures, focusing on measurement efficiency and minimal data requirements.

Findings

Provides a generalized framework for entropy calculation using ordinal partitions.

Analyzes the minimal number of measurements needed for accurate entropy estimation.

Focuses on measure-preserving dynamical systems without information loss.

Abstract

The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of determining the Kolmogorov-Sinai entropy of a measure-preserving dynamical system via increasing sequences of order generated partitions of the state space. Our main focus are measuring processes without information loss. Particularly, we consider the question of the minimal necessary number of measurements related to the properties of a given dynamical system.