Stabilities of generalized entropies

TL;DR

This paper investigates the stability of generalized entropies under specific constraints, deriving conditions for stability and discussing examples like stretched-exponential, quantum-group, and kappa-entropies.

Contribution

It provides a general stability condition for generalized entropies, expanding understanding beyond thermodynamic stability and analyzing various known entropy forms.

Findings

Derived a general stability condition for generalized entropies

Analyzed stability of specific entropies like stretched-exponential and kappa-entropy

Discussed implications of Lesche stability in different entropy models

Abstract

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its Lesche stability property (that is different from thermodynamic stability) is examined. A general condition, under which the generalized entropy becomes stable, is derived. Examples known in the literature, including the entropy for the stretched-exponential distribution, the quantum-group entropy, and the kappa-entropy are discussed.