ON THE EINSTEIN RELATION FOR A MECHANICAL SYSTEM

We consider a mechanical model in the plane, consisting of a vertical rod, subject to a constant horizontal force f and to elastic collision s with the particles of a free gas which is ''horizontally'' in equili brium at some inverse temperature beta. In a previous paper we proved that, in the appropriate space and time scaling, the motion of the rod is described as a drift ten plus a diffusion term. In this paper we p rove that the drift d(f) and the diffusivity sigma(2)(f) are continuou s functions of f, and moreover that the Einstein relation holds, i.e., lim/(f-->0) d(f)/f = beta/2 sigma(2) (0).