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 Δstot. One is the entropy production of the medium Δsm, 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 Δstot. Differently, for large values of E, the fluctuations of W violate the FR, while Δsmstill verifies it. © 2012 American Physical Society.
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