2014/04/30 by Daniel Hurowitz, Doron Cohen
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Asymmetry #Brownian motion #Classical mechanics #Economics #Einstein #Einstein relation #Mathematics #Non-equilibrium thermodynamics #Nonlinear system #Physics #Quantum mechanics #Randomness #Statistical Mechanics and Entropy #Statistical physics #Statistics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.90.032129
published as Phys. Rev. E 90, 032129 (2014) · 9 pages, 4 figures, an improved version with an additional section
arxiv created 2014/09/18 · openalex publication_date 2014/09/22 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.