Entropies based on fractional calculus

TL;DR

This paper introduces a new class of entropy functions derived from fractional calculus, which are non-extensive but satisfy key stability criteria, expanding the theoretical framework of entropy measures.

Contribution

The paper presents a novel entropy based on fractional calculus that retains many properties of Shannon entropy but is non-additive, offering a new perspective on non-extensive entropy.

Findings

Entropy is non-extensive due to lack of additivity.

The entropy satisfies Lesche stability.

The entropy meets thermodynamic stability criteria.

Abstract

We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except additivity, therefore making this entropy non-extensive. We show that this entropy function satisfies the Lesche and thermodynamic stability criteria.