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A consistent generalization of statistical mechanics is obtained by applyingthe maximum entropy principle to a trace-form entropy and by requiring thatphysically motivated mathematical properties are preserved. The emergingdifferential-functional equation yields a two-parameter class of generalizedlogarithms, from which entropies and power-law distributions follow: thesedistributions could be relevant in many anomalous systems. Within the specifiedrange of parameters, these entropies possess positivity, continuity, symmetry,expansibility, decisivity, maximality, concavity, and are Lesche stable. TheBoltzmann-Shannon entropy and some one parameter generalized entropies alreadyknown belong to this class. These entropies and their distribution functionsare compared, and the corresponding deformed algebras are discussed.Comment: Version to appear in PRE: about 20% shorter, references updated, 13  PRE pages, 3 figure

Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics