Abstract.
We consider a mechanical model in the plane, consisting of a vertical rod, subject to a constant horizontal force f and to elastic collisions with the particles of a free gas which is “horizontally” in equilibrium at some inverse temperature β. In a previous paper we proved that, in the appropriate space and time scaling, the motion of the rod is described as a drift term plus a diffusion term. In this paper we prove that the drift d(f) and the diffusivity σ 2 (f) are continuous functions of f, and moreover that the Einstein relation holds, i.e.,
lim f → 0 d(f)f = β2 σ 2 (0) .
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Received: 26 January 1996 / In revised form: 2 October 1996
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Boldrighini, C., Soloveitchik, M. On the Einstein relation for a mechanical system. Probab Theory Relat Fields 107, 493–515 (1997). https://doi.org/10.1007/s004400050095
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DOI: https://doi.org/10.1007/s004400050095
- Mathematics Subject Classification (1991): 60K35
- 60J27 or 82C05 and 82C31