Work fluctuations for a Brownian particle between two thermostats

We explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures. This toy model, initially introduced by Derrida and Brunet [B. Derrida and E. Brunet, in "Einstein aujourd'hui", EDP Sciences, 2005], allows not only to sort out the influence of initial conditions on large deviation functions but also to pinpoint various restrictions bearing upon the range of validity of the Fluctuation Relation.