Nonequilibrium statistical description of anomalous diffusion

In this paper, from the unifying viewpoint we will cover our recent work on the nonequilibrium statistical description of anomalous diffusion and application of this theory to explaining late experiment. We will study the motion of a particle under the influence of a random force modeled as Gaussian colored noise with arbitrary correlation and with/without external field. In the very general case, the generalized Langevin equation is presented. We obtain the variances of displacement, velocity and cross variance between displacement and velocity, their asymptotic and crossover behavior. The exact equations for the joint and marginal probability density functions, and their solutions are obtained. Finally the anomalous diffusion is described in the framework of nonequilibrium statistical mechanics. The experimental results (Skjeltorp et al., Phys. Rev. E 58 (1998) 4229) can well be explained by our theory presented in this paper.