Kinetic model for q-deformed bosons and fermions

We have studied the kinetics of q-deformed bosons and fermions, within a semiclassical approach. This investigation is realized by introducing a generalized exclusion-inclusion principle, intrinsically connected with the quantum q-algebra by means of the creation and annihilation operator matrix elements. In this framework, we have derived a nonlinear Fokker-Planck equation for q-deformed bosons and fermions which can be seen as a time evolution equation, appropriate to consider nonequilibrium or near-equilibrium systems in a semiclassical approximation. The steady state of this equation reproduces in a simple mode the q-oscillators equilibrium statistics.