Current fluctuations in stochastic lattice gases

We study current ßuctuations in lattice gases in the macroscopic limit extending the dynamic approach for density ßuctuations developed in previous articles. More precisely, we establish a large deviation theory for the space-time ßuctuations of the empirical current which include the previous results. We then estimate the probability of a ßuctuation of the average current over a large time interval. It turns out that recent results by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)] in certain cases underestimate this probability due to the occurrence of dynamical phase transitions