Entropic Forms and Related Algebras

TL;DR

This paper introduces algebraic structures based on generalized entropy forms, establishing their properties and applications to various distributions observed in complex systems across multiple disciplines.

Contribution

It develops new algebraic frameworks from trace-form entropies and applies them to distributions in social, economic, biological, and physical systems.

Findings

The algebraic structures form two isomorphic Abelian fields over complex numbers.

Applicable to distributions like stretched exponential, power-law, and Bosons-Fermions.

Potential applications in analyzing complex systems are proposed.

Abstract

Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.