On the statistical interpretation of generalized entropies

We present a direct generalization of the Boltzmann counting method to define a generic form for a generalized entropy. This form is based on the probabilities of sequences of a stochastic process. Usual forms of generalized entropy can be rewritten in our approach, and then be reinterpreted on a statistical basis. We also discuss the meaning of temperature and the zeroth-law of thermodynamics. Renyi and Tsallis entropies are used to illustrate our approach. Monte Carlo simulations of the corresponding stochastic processes are performed and the results corroborate the approach. (c) 2005 Elsevier B.V. All rights reserved.