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We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation theory for the space-time fluctuations of the empirical current which include the previous results. We then estimate the probability of a fluctuation 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.
Bertini et al. (Tue,) studied this question.
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