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Non-equilibrium 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 E 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 Δs_tot. One is the entropy production of the medium Δs_m, which is equal to the energy exchanged with the scatterers, divided by a parameter θ, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by θ. At small E, 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 Δs_tot. Differently, for large values of E, the fluctuations of W violate the FR, while Δs_m still verifies it.