We discuss the transient and steady state fluctuation relation for amechanical system in contact with two deterministic thermostats at differenttemperatures. The system is a modified Lorentz gas in which the fixedscatterers exchange energy with the gas of particles, and the thermostats aremodelled by two Nos\'e-Hoover thermostats applied at the boundaries of thesystem. The transient fluctuation relation, which holds only for a precisechoice of the initial ensemble, is verified at all times, as expected. Timeslonger than the mesoscopic scale, needed for local equilibrium to be settled,are required if a different initial ensemble is considered. This shows how thetransient fluctuation relation asymptotically leads to the steady staterelation when, as explicitly checked in our systems, the condition found in[D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validityof the steady state fluctuation relation, is verified. For the steady statefluctuations of the phase space contraction rate $\zL$ and of the dissipationfunction $\zW$, a similar relaxation regime at shorter averaging times isfound. The quantity $\zW$ satisfies with good accuracy the fluctuation relationfor times larger than the mesoscopic time scale; the quantity $\zL$ appears tobegin a monotonic convergence after such times. This is consistent with thefact that $\zW$ and $\zL$ differ by a total time derivative, and that the tailsof the probability distribution function of $\zL$ are Gaussian.
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