Is the Tsallis entropy stable?

¹  Center for Nonlinear Phenomena and Complex Systems, CP 231, Université Libre de Bruxelles 1050 Brussels, Belgium, EU
²  Microgravity Research Center, Chimie Physique E.P., CP 165/62, Université Libre de Bruxelles Av. F. D. Roosevelt 50, 1050 Brussels, Belgium, EU

Corresponding author: jlutsko@ulb.ac.be

Received: 26 February 2009
Accepted: 30 April 2009

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.