A counterexample against the Lesche stability of a generic entropy functional

Aziz El Kaabouchi (1) , Qiuping A. Wang (1) , C.J. Ou (1) , Jincan Chen (1) , Guozhen Su (1) , Alain Le Méhauté (1)

1 ISMANS CESI - Institut Supérieur des Mécaniques et Matériaux Avancés

We provide a counterexample to show that the generic form of entropy S(p)=sum_i g(p_i) is not always stable against small variation of probability distribution (Lesche stability) even if is concave function on [0,1] and analytic on ]0,1]. Our conclusion is that the stability of such a generic functional needs more hypotheses on the property of the function g, or in other words, the stability of entropy cannot be discussed at this formal stage.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Aziz El Kaabouchi, Qiuping A. Wang, C.J. Ou, Jincan Chen, Guozhen Su, et al.. A counterexample against the Lesche stability of a generic entropy functional. 2009. ⟨hal-00364278⟩