  We study nonequilibrium steady states of lattice gases with nearest-neighbor
interactions that are driven between two reservoirs. Density profiles in these
systems exhibit oscillations close to the reservoirs. We demonstrate that an
approach based on time-dependent density functional theory copes with these
oscillations and predicts phase diagrams of bulk densities to a good
approximation under arbitrary boundary-reservoir couplings. The minimum or
maximum current principles can be applied only for specific bulk-adapted
couplings. We show that they generally fail to give the correct topology of
phase diagrams but can still be useful for getting insight into the mutual
arrangement of different phases.
