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arXiv · 0903.4169

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
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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.

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Aziz El Kaabouchi, Qiuping A. Wang, C. J. Ou, Jincan Chen, Guozhen Su, Alain Le Méhauté. 2009-03-24. A counterexample against the Lesche stability of a generic entropy functional. https://doi.org/10.1063/1.3589845

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