A counterexample against the Lesche stability of a generic entropy functional

Aziz El Kaabouchi; Qiuping A. Wang; C. J. Ou; Jincan Chen; Guozhen Su; Alain Le Méhauté

doi:10.1063/1.3589845

paper

A counterexample against the Lesche stability of a generic entropy functional

arXiv:0903.4169 · doi:10.1063/1.3589845

Abstract

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.