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We study entropy rates of random sequences for general entropy functionals including the classical Shannon and Rényi entropies and the more recent Tsallis and Sharma-Mittal ones. In the first part, we obtain an explicit formula for the entropy rate for a large class of entropy functionals, as soon as the process satisfies a regularity property known in dynamical systems theory as the quasi-power property. Independent and identically distributed sequence of random variables naturally satisfydoi:10.1109/tit.2011.2133710 fatcat:3zfkvmgmxjfsfe5bzuh47u3zdy