CLASSICAL-MODEL OF BOSON AND FERMIONS

In a previous work [Phys. Rev. E 48, 4263 (1993)] we have derived a no nlinear one-dimensional kinetic equation for the distribution function of particles obeying an exclusion principle. In the present work, on the same grounds, we extend this kinetics to D-dimensional continuous or discrete space, in order to study the distribution function of part icles obeying a generalized exclusion-inclusion Pauli principle (EIP). This exclusion or inclusion principle is introduced into the classica l transition rates by means of an inhibition or an enhancement factor, which contains a parameter kappa, whose values range between -1 and 1 and can balance the effect of the full or partial validity of EIP. A fter deriving the kinetic equation we obtain a general expression of t he stationary distribution function depending on the value we give to the parameter kappa. When we limit ourselves to Brownian particles, we derive exactly for kappa = -1 the Fermi-Dirac (FD) distribution, for kappa = 0 the Maxwell-Boltzmann distribution, and for kappa = 1 the Bo se-Einstein (BE) distribution. When kappa assumes an intermediate valu e, except zero, between the extreme values -1 and +1, we obtain statis tical distributions different from the FD and BE ones. We attribute to the parameter kappa the meaning of the degree of indistinguishability of identical particles, the degree of antisymmetrization, or the symm etrization of the wave function of the particle system.