Deformed logarithms and entropies

TL;DR

This paper introduces a new two-parameter family of deformed logarithms and entropies derived from a differential-functional equation, unifying and generalizing existing entropy measures within a broad theoretical framework.

Contribution

It derives a novel two-parameter class of deformed logarithms and entropies, encompassing many existing generalizations as special cases, based on solving a differential-functional equation.

Findings

Identifies parameter regions where the deformed logarithm retains key properties.

Shows that classical Shannon entropy is a special case within this family.

Includes known entropy generalizations as specific instances.

Abstract

By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.