Towards an Information Geometric characterization/classification of Complex Systems. II. Critical Parameter values from the (c,d)-manifold

TL;DR

This paper introduces a new geometric approach to classify complex systems using the (c,d)-parameters as coordinates on an information manifold, linking scalar curvature to system behavior and addressing boundary singularities.

Contribution

It proposes a novel geometric framework for characterizing complex systems via (c,d) parameters as coordinates, providing insights into their behavior and boundary regularization.

Findings

Scalar curvature characterizes complex system behavior.

Boundary values of (c,d) are singular, requiring regularization.

The (c,d)-manifold simplifies analysis of complex systems.

Abstract

In our previous paper (I) we derived information geometric objects from the two parameter generalized entropy of Hanel and Thurner (2011), using the c,d parameters as labels of the corresponding manifolds. Here we follow a completely different approach by considering these parameters as coordinates of our information manifolds. This gives a manageable two-dimensional manifold amenable to easy manipulations but most importantly it offers a direct characterization of complex systems in terms of the pair of the c,d values. As a result we obtain certain characteristic values from the scalar curvature which we could conjecture that they represent complex systems with specific behavior. It is further observed that the boundary values of the c,d parameters which characterize the Hanel-Thurner classification are in some sense singular. This asks for a regularization scheme which we try to establish.