Non-equilibrium version of the Einstein relation

Abstract

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. Hence it depends in a non-trivial way on the microscopics of the sample.

9 pages, 4 figures, an improved version with an additional section

References in corpus (7)

• The Einstein relation generalized to non-equilibrium
• Giant Colloidal Diffusivity on Corrugated Optical Vortices
• Fluctuation relations and coarse-graining
• Weak disorder strongly improves the selective enhancement of diffusion in a tilted periodic potential
• Characterizing Potentials by a Generalized Boltzmann Factor
• Fluctuation Theorem and Microreversibility in a Quantum Coherent Conductor
• Non-equilibrium steady state of sparse systems