Is the Tsallis entropy stable?

TL;DR

This paper investigates the Lesche stability of Tsallis entropy, showing it is unstable under certain conditions, but thermodynamic averages remain stable, and proposes homogeneous entropy as a more stable alternative.

Contribution

It clarifies the conditions under which Tsallis entropy is Lesche-stable and introduces homogeneous entropy as a stable foundation for non-extensive thermodynamics.

Findings

Tsallis entropy is unstable with escort probabilities

Thermodynamic averages remain stable despite entropy instability

Homogeneous entropy achieves Lesche and thermodynamic stability

Abstract

The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.