Nonequilibrium statistical mechanics of drifting particles

Abstract

This paper describes a method for obtaining nonequilibrium one-particle energy distributions of fermions or bosons. For the program to be carried out, particle transport should occur in the drifting mode in which the average velocity is much lower than the instantaneous velocity. Under this condition, the spectral current density has a drift-diffusion structure involving a mobility-diffusion relationship unrelated to statistics. When a local-equilibrium energy distribution is used, the linear response theory is recovered. Next, the particle-medium energy exchange is treated within a Fokker-Planck framework in order to obtain the nonequilibrium energy distribution; a nonlinear framework is used to account for the quantum-statistical correlations. Explicit formulas are obtained for homogeneous distributions at steady state. The rate of change of entropy is a simple generalization of the second law of thermodynamics. The positivity of the total entropy production stems from the positive definiteness of the diffusion tensors. Minimal entropy production is not necessarily achieved in the stationary state.