On a comparative study between dependence scales determined by linear and non-linear measures

TL;DR

This study compares linear and non-linear dependence measures to determine relaxation time scales, revealing that non-linear measures are more suitable for complex systems, while simpler systems show similar results across methods.

Contribution

It introduces a comparative analysis of dependence scales using correlation, mutual information, and a nonextensive entropy-based criterion for different system complexities.

Findings

For simple systems, both measures yield similar time scales.

In complex systems, non-linear measures indicate larger time scales.

Standard mutual information underestimates dependence in complex dynamics.

Abstract

In this manuscript we present a comparative study about the determination of the relaxation (\textit{i.e.}, independence) time scales obtained from the correlation function, the mutual information, and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy. Our results show that, for systems with a small degree of complexity, standard mutual information and the criterion based on its nonextensive generalisation provide the same scale, whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller.