Classical bosons and fermions in the contemporary transition description

Contemporary transition description, in the nearest neighbors frame, allows a more complete and rigorous treatment of the kinetics of a system of identical particles obeying an exclusion-inclusion principle than the only individual transition approximation. Within this description, statistical distributions are derived, as stationary states of a generalized non linear Fokker-Planck equation, and collective quantum macroscopic effects for both bosons and fermions can be evidentiated in a more precise form and with a more appropriate meaning than in the indidual transition approximation.