Large deviations for currents in the spin-boson model

We consider a finite quantum system coupled to quasifree thermal reservoirs at different temperatures. Under the assumptions of small coupling and exponential decay of the reservoir correlation function, the large deviation generating function is shown to be analytic on a compact set. Our method is different from the spectral deformation technique which was introduced recently in the study of spinboson-like models. As a corollary, we derive the Gallavotti-Cohen fluctuation relation for the entropy production.