Complexity measures, emergence, and multiparticle correlations

TL;DR

This paper critically examines existing correlation measures for complex systems, revealing their limitations under local transformations, and proposes refined measures with applications to coupled logistic maps and coarse graining effects.

Contribution

It introduces a refined definition of correlation measures, analyzes their properties, and demonstrates their behavior through numerical studies on coupled logistic maps.

Findings

Existing measures can increase under local transformations

Refined measures provide more consistent quantification of complexity

Numerical analysis on logistic maps illustrates measure behavior

Abstract

We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding particles, thereby questioning their interpretation as a quantifier for complexity or correlations. We then propose a refined definition of these measures, investigate its properties and discuss its numerical evaluation. As an example, we study coupled logistic maps and study the behavior of the different measures for that case. Finally, we investigate other local effects during the coarse graining of the complex system.