A statistical mechanical approach to generalized statistics of quantum and classical gases

Abstract For many particle non-interacting gases which are in heat and particle baths the grand canonical ensemble concept has been set out. The set of occupation numbers of the R quantum states of the gas is described by { n 1 , n 2 , …, n k , …}. As the entropy of the ensemble, one of the fractal inspired entropies, namely Tsallis entropy, has been considered and expressed for the ensemble. The probability P R of the ensemble to be in the state R has been investigated for the equilibrium state, by making use of the Boltzmann H -theorem with the techniques of calculus of variations. Having obtained the probability P R , the generalized distribution functions of the quantum gases have been established. On the other hand, the generalized distribution functions of the classical gases have been found as a special case of one of the quantum gases, namely the boson gas.