Nonequilibrium fluctuations in a driven stochastic Lorentz gas

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field epsilon and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production Delta s(tot). One is the entropy production of the medium Delta s(m), which is equal to the energy exchanged with the scatterers, divided by a parameter theta, coinciding with the particle temperature at epsilon = 0. The other is the work W done by the external field, again rescaled by theta. At small epsilon, a good collapse of the two distributions is found: in this case, the two quantities also verify the fluctuation relation (FR), indicating that both are good approximations of Delta s(tot). Differently, for large values of epsilon, the fluctuations of W violate the FR, while Delta s(m) still verifies it.