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. 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 2(f) are continuous functions of f, and moreover that the Einstein relation holds.
On the Einstein relation for a mechanical system / Boldrighini, Carlo; M., Soloveichik. - In: PROBABILITY THEORY AND RELATED FIELDS. - ISSN 0178-8051. - STAMPA. - 107:4(1997), pp. 493-515. [10.1007/s004400050095]
On the Einstein relation for a mechanical system
BOLDRIGHINI, Carlo;
1997
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. 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 2(f) are continuous functions of f, and moreover that the Einstein relation holds.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
