GENERALIZATION OF QUANTUM STATISTICS IN STATISTICAL-MECHANICS

We propose a generalization of quantum statistics in the framework of statistical mechanics. We derive a general formula which involves a wide class of equilibrium quantum statistical distributions, including the Bose and Fermi distributions. We suggest a way of evaluating the statistical distributions with the help of many-particle partition functions and apply it to studying some interesting distributions. A question on the statistical distribution for anyons is discussed, and the term following the Boltzmann one in the expansion of this distribution in powers of the Boltzmann factor, exp[beta(mu - epsilon(i))], is estimated. An ansatz is proposed for evaluating the statistical distribution for quons (particles whose creation and annihilation operators satisfy the q-commutation relations). We also treat nonequilibrium statistical mechanics, obtaining unified expressions for the entropy of a nonequilibrium quantum gas and for a collision integral which are valid for a wide class of statistics.