A counterexample against the Lesche stability of a generic entropy functional
Statistical Mechanics
2020-10-21 v1
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.
Keywords
Cite
@article{arxiv.0903.4169,
title = {A counterexample against the Lesche stability of a generic entropy functional},
author = {Aziz El Kaabouchi and Qiuping A. Wang and C. J. Ou and Jincan Chen and Guozhen Su and Alain Le Méhauté},
journal= {arXiv preprint arXiv:0903.4169},
year = {2020}
}