On the stability of analytic entropic forms

The stability against small perturbations on the probability distributions (also called experimental robustness) of analytic entropic forms is analyzed. Entropies S[p], associated with a given set of probabilities {pi}, that can be written in the simple form S[p]=∑i=1W r(pi), are shown to be robust, if r(pi) is an analytic function of the piʹs. The same property holds for entropies Σ(S[p]) that are monotonic and analytic functions of S[p]. The Tsallis entropy Sq[p] falls in the first class of entropies, whenever the entropic index q is an integer greater than 1. A new kind of entropy, that follows such requirements, is discussed.