  One-dimensional, boundary-driven lattice gases with local interactions are
studied in the weakly interacting limit. The density profiles and the
correlation functions are calculated to first order in the interaction strength
for zero-range and short-range processes differing only in the specifics of the
detailed-balance dynamics. Furthermore, the effective free-energy
(large-deviation function) and the integrated current distribution are also
found to this order. From the former, we find that the boundary drive generates
long-range correlations only for the short-range dynamics while the latter
provides support to an additivity principle recently proposed by Bodineau and
Derrida.
