Properties of the Nonextensive Gaussian entropy

TL;DR

This paper explores the properties of the nonextensive Gaussian entropy, demonstrating its stability, thermodynamic consistency, and deriving its maximum entropy distribution involving Lambert W-function, thus supporting its theoretical robustness.

Contribution

It introduces and analyzes the nonextensive Gaussian entropy, establishing its stability and thermodynamic structure, and deriving its maximum entropy distribution with Lambert W-function.

Findings

The entropy is stable for all parameter values.

It maintains the Legendre structure of thermodynamics.

The maximum entropy distribution involves Lambert W-function.

Abstract

The present work investigates the Lesche stability (experimental robustness), the thermodynamic stability, the Legendre structure of thermodynamics, and derives the Maximum Entropy distribution of the one--parametric ``nonextensive Gaussian'' entropy. We show that this entropy definition fulfills both stability conditions for all values of its parameter ($q\in\mathbb{R}$). The entropy maximizer contains the Lambert $W$--function, which allows the preservation of the Legendre transformations.