Abstract
Recently, Santos obtained a generalized entropy using four assumptions which stated that an entropy must: (i) be a continuous function of the probabilities ; (ii) be a monotonic increasing function of the number of states W, in the case of equiprobability; (iii) satisfy (where A and B are two independent systems) and (iv) satisfy the relation , where ( and ). Santos showed that the only function which satisfies all of these properties is the generalized Tsallis entropy. In this paper we perform a similar analysis and we obtain a family of entropies which are equivalent to the Tsallis entropy. We also discuss the Shannon inequality in the context of the generalized Tsallis entropy.
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