Entropic descriptor of a complex behaviour

TL;DR

This paper introduces a novel entropic descriptor that quantifies statistical complexity by considering entropy deviations from both maximum and minimum values, effectively distinguishing complex spatial patterns across scales.

Contribution

The paper presents a new entropic complexity measure that accounts for entropy deviations from both bounds, enhancing the analysis of structural complexity in patterns.

Findings

The entropic descriptor effectively captures length-scale dependent complexity.

It distinguishes between structurally different configurations with similar disorder.

The measure is validated on simple models of spatial and grey-level patterns.

Abstract

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum possible value Smax and its minimum possible value Smin. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length-scale dependence of the entropic descriptor makes it an adequate complexity-measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder.