Non-thermal Einstein relations
1 Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique F-69342 Lyon, France
2 Department of Mathematics and Statistics, The Open University - Walton Hall, Milton Keynes, MK7 6AA, UK
Received: 18 February 2016
Accepted: 18 July 2016
We consider a particle moving with equation of motion , where f(t) is a random function with statistics which are independent of x and t, with a finite drift velocity and in the presence of a reflecting wall. Far away from the wall, translational invariance implies that the stationary probability distribution is . A classical example of a problem of this type is sedimentation equilibrium, where α is determined by temperature. In this work we do not introduce a thermal reservoir and α is determined from the equation of motion. We consider a general approach to determining α which is not always in agreement with Einstein's relation between the mean velocity and the diffusion coefficient. We illustrate our results with a model inspired by the Boltzmann equation.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2016