Diffusion and mobility and generalized Einstein relation

The general response theory to thermal perturbations presented in the preceding paper is applied to a simple model. We obtain the evolution equation for the particle density, which becomes of the form of a propagating wave with a damping dependent on the diffusion coefficient. The latter is calculated at the microscopic level. For a charged system we also determine the mobility coefficient for arbitrarily intense electric fields, obtaining a generalized Ohmʹs law for nonlinear charge transport. Using the expressions for both transport coefficients we derive the Einstein relation in the nonlinear nonequilibrium thermodynamic state of the system.