Volume 86, Number 4, May 2009
Article Number 40005
Number of page(s) 6
Section General
Published online 05 June 2009
EPL, 86 (2009) 40005
DOI: 10.1209/0295-5075/86/40005

Is the Tsallis entropy stable?

J. F. Lutsko1, J. P. Boon1 and P. Grosfils1, 2

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

received 26 February 2009; accepted in final form 30 April 2009; published May 2009
published online 5 June 2009

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.

05.20.-y - Classical statistical mechanics.
02.50.Cw - Probability theory.

© EPLA 2009