Fluctuations relation and external thermostats: an application to   granular materials
  In this note we discuss a paradigmatic example of interacting particles subject to non conservative external forces and to the action of thermostats consisting of external (finite) reservoirs of particles. We then consider a model of granular materials of interest for experimental tests that had recently attracted lot of attentions. This model can be reduced to the previously discussed example under a number of assumptions, in particular that inelasticity due to internal collisions can be neglected for the purpose of measuring the large deviation functional for entropy production rate. We show that if the restitution coefficient in the granular material model is close to one, then the required assuptions are verified on a specific time scale and we predict a fluctuation relation for the entropy production rate measured on the same time scale. 
F.Bonetto, G.Gallavotti, A.Giuliani, F.Zamponi