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 operators matrix elements. In this framework, we have derived a non-linear Fokker-Planck equation for $q$-deformed bosons and fermions which can be seen as a time evolution equation, appropriate to consider non-equilibrium or near-equilibrium systems in a semiclassical approximation. The steady state of this equation reproduces in a simple mode the $q$-oscillators equilibrium statistics.