Extensive form of equilibrium nonextensive statistics

It is argued that, in nonextensive statistical mechanics with Tsallis entropy, the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system and should be respected by all exact calculations concerning equilibrium subsystems. Using nonadditive energy satisfying this factorization, we propose an additive formalism of nonextensive statistical mechanics with additive q-deformed physical quantities and exponential distributions. This formalism leads to exact quantum gas distributions different from those given by factorization approximation with additive energy. The fermion distribution of the present work shows similar characteristics to the distribution of strongly correlated electrons given by numerical analysis with the Kondo t-J model.