Multivariate Group Entropies, Super-exponentially Growing Complex Systems and Functional Equations

TL;DR

This paper introduces multivariate group entropies as a new class of information measures, explores their connection to super-exponential complex systems, and demonstrates their application in exactly solvable dynamical models using formal group theory.

Contribution

It extends the family of group entropies with multivariate versions and links them to super-exponential systems and solvable models via formal group theory.

Findings

Defined multivariate group entropies as a new information measure.

Linked these entropies to super-exponential complex systems.

Developed a family of exactly solvable dynamical models.

Abstract

We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality class of complex systems; in particular, we introduce a general entropy, representing a suitable information measure for this class. We also show that the group-theoretical structure associated with our multivariate entropies can be used to define a large family of exactly solvable discrete dynamical models. The natural mathematical framework allowing us to formulate this correspondence is offered by the theory of formal groups and rings.