  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 \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 E=0. The other is the work W done by the external field, again
rescaled by \theta. 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 \Delta s_tot.
Differently, for large values of E, the fluctuations of W violate the FR, while
\Delta s_m still verifies it.
