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.