Lesche Stability of $\kappa$-Entropy

TL;DR

This paper proves that the recently introduced $ppa$-entropy satisfies the Lesche stability condition, ensuring its robustness and suitability as an entropic measure for non-conventional statistical mechanics.

Contribution

It demonstrates that the $ppa$-entropy fulfills the Lesche stability criterion, a key test for the physical robustness of entropic functionals.

Findings

$ppa$-entropy satisfies Lesche stability

Supports $ppa$-entropy as a robust statistical measure

Validates $ppa$-entropy for non-conventional systems

Abstract

The Lesche stability condition for the Shannon entropy [B. Lesche, J. Stat. Phys. 27, 419 (1982)], represents a fundamental test, for its experimental robustness, for systems obeying the Maxwell-Boltzmann statistical mechanics. Of course, this stability condition must be satisfied by any entropic functional candidate to generate non-conventional statistical mechanics. In the present effort we show that the $\kappa$-entropy, recently introduced in literature [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002)], satisfies the Lesche stability condition.