The celebrated Einstein relation between the diffusion coefficient $D$ and the drift velocity $v$ is violated in nonequilibrium 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 nonequilibrium fluctuation theorem the $v/D$ ratio is found to be a nonlinear function of the affinity. Hence it depends in a nontrivial way on the microscopics of the sample.

• Received 30 April 2014
• Revised 19 June 2014

DOI:https://doi.org/10.1103/PhysRevE.90.032129