Towards an Information Geometric characterization/classification of Complex Systems. I. Use of Generalized Entropies

TL;DR

This paper introduces a geometric framework using two-parameter generalized entropies to classify complex systems, establishing fundamental geometric objects and inequalities, and providing a new classification method based on information geometry.

Contribution

It constructs a two-parameter family of probability distributions and derives associated geometric objects, including a metric and scalar curvature, for classifying complex systems.

Findings

Established existence of a two-parameter family of distributions

Derived a generalized Cramer-Rao inequality

Provided a geometric classification based on scalar curvature

Abstract

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing some fundamental geometric objects. We first establish the existence of a two-parameter family of probability distributions. Then using this family we derive the associated metric and we state a generalized Cramer-Rao inequality. This gives a first two-parameter classification of complex systems. Finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes. Our analysis is based on the two-parameter family of generalized entropies of Hanel and Thurner (2011)