Nonadditive statistical measure of complexity and values of the entropic index q

TL;DR

This paper introduces a two-parameter family of complexity measures based on Tsallis entropy, unifying various existing measures and exploring their behavior in dynamical systems like the logistic map.

Contribution

It develops a generalized framework for complexity measures using Tsallis entropy and analyzes the optimal entropic index q at the edge of chaos.

Findings

Maximum complexity occurs at the edge of chaos for specific q values.

The framework unifies existing complexity measures under a common formalism.

Behavior of the complexity measure is illustrated with the logistic map.

Abstract

A two-parameter family of statistical measures of complexity are introduced based on the Tsallis-type nonadditive entropies. This provides a unified framework for the study of the recently proposed various measures of complexity as well as for the discussion of a whole new class of measures. As a special case, a generalization of the measure proposed by Landsberg and his co-workers based on the Tsallis entropy indexed by q is discussed in detail and its behavior is illustrated using the logistic map. The value of the entropic index, q, with which the maximum of the measure of complexity is located at the edge of chaos, is calculated.