The authors derive the equation of evolution in the configuration space for a system of semiclassical bosons or fermions starting from the recently derived nonlinear Kramers-Chandrasekhar equation for such particles. The latter equation does not contract to the corresponding Fokker-Planck equation in the velocity space; however, it is shown that in the context of a Chapman-Enskog approximation the contraction to the physical space leads to the diffusion equation with the classical relationship between the self-diffusion coefficient and the friction coefficient maintained.
The soluble model of an oscillator coupled to a scalar field is used as an example of irreversible behavior. By studying the reduced density operator for the oscillator, a generalized Fokker-Planck-Kramers-Chandrasekhar equation for the Wigner distribution function is derived. The diagonal matrix elements of the reduced density operator satisfy a generalized non-Markovian master equation. By application of a time-averaged method, the ordinary Pauli master equation is derived. The time evolution of the occupation probabilities of the oscillator levels has been numerically computed, and compared with the solutions of the Pauli equation.