A basic problem in the correlations between statistics and thermodynamics

By using a functional of probability distributions, several different statistical physics including extensive and nonextensive statistics are unified in a general formalism. It’s shown that the equivalence between the Maxent approach and the relation dU = TdS can be seen from the virtual work principle of mechanics. From dU = TdS, any entropic form which can exists for thermodynamical equilibrium system can be maximized in order to derive the probability distribution functions.