Non equilibrium version of the Einstein relation

The celebrated Einstein relation between the diffusion coefficient D and the drift velocity v is violated in non equilibrium circumstances We analyze how this violation emerges for the simplest example of a Brownian motion on a lattice taking into account the interplay between the periodicity the randomness and the asymmetry of the transition rates Based on the non equilibrium fluctuation theorem the v D ratio is found to be a non linear function of the affinity 1 D Hurowitz and D Cohen