A STATISTICAL-MECHANICAL APPROACH TO GENERALIZED STATISTICS OF QUANTUM AND CLASSICAL GASES

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 T sallis entropy, has been cons idered and expressed for the ensemble. The probability P-R of the ense mble to be in the slate R has been investigated for the equilibrium st ate, by making use of the Boltzmann H-theorem with the techniques of c alculus of variations. Having obtained the probability P-R, the genera lized distribution functions of the quantum gases have been establishe d. On the other hand, the generalized distribution functions of the cl assical gases have been found as a special case of one of the quantum gases, namely the boson gas.