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

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Cited by in corpus (4)

• Transient photocurrent and optical absorption of disordered thin-film semiconductors: in-depth injection and nonlinear response
• Percolation, sliding, localization and relaxation in topologically closed circuits
• The relaxation rate of a stochastic spreading process in a closed ring
• Negative mobility, sliding and delocalization for stochastic networks