A counterexample against the Lesche stability of a generic entropy functional

Details A counterexample against the Lesche stability of a generic entropy functional A counterexample against the Lesche stability of a generic entropy functional

2009-03-24

arxiv.org/abs/0903.4169v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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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