Is the Tsallis entropy stable?

Details Is the Tsallis entropy stable? Is the Tsallis entropy stable?

2009-02-26

arxiv.org/abs/0902.4579v1

2009 Europhys. Lett. 86 40005

Physics

Condensed Matter

Statistical Mechanics

6 pages

Scientific paper

10.1209/0295-5075/86/40005

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.

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