  We study current fluctuations in lattice gases in the hydrodynamic scaling
limit. More precisely, we prove a large deviation principle for the empirical
current in the symmetric simple exclusion process with rate functional I. We
then estimate the asymptotic probability of a fluctuation of the average
current over a large time interval and show that the corresponding rate
function can be obtained by solving a variational problem for the functional I.
For the symmetric simple exclusion process the minimizer is time independent so
that this variational problem can be reduced to a time independent one. On the
other hand, for other models the minimizer is time dependent. This phenomenon
is naturally interpreted as a dynamical phase transition.
