  We consider an open one dimensional lattice gas on sites $i=1,...,N$, with
particles jumping independently with rate 1 to neighboring interior empty
sites, the {\it simple symmetric exclusion process}. The particle fluxes at the
left and right boundaries, corresponding to exchanges with reservoirs at
different chemical potentials, create a stationary nonequilibrium state (SNS)
with a steady flux of particles through the system. The mean density profile in
this state, which is linear, describes the typical behavior of a macroscopic
system, i.e., this profile occurs with probability 1 when $N \to \infty$. The
probability of microscopic configurations corresponding to some other profile
$\rho(x)$, $x = i/N$, has the asymptotic form $\exp[-N {\cal F}(\{\rho\})]$;
$\cal F$ is the {\it large deviation functional}. In contrast to equilibrium
systems, for which ${\cal F}_{eq}(\{\rho\})$ is just the integral of the
appropriately normalized local free energy density, the $\cal F$ we find here
for the nonequilibrium system is a nonlocal function of $\rho$. This gives rise
to the long range correlations in the SNS predicted by fluctuating
hydrodynamics and suggests similar non-local behavior of $\cal F$ in general
SNS, where the long range correlations have been observed experimentally.
