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We study nonequilibrium steady states of lattice gases with nearest-neighborinteractions that are driven between two reservoirs. Density profiles in thesesystems exhibit oscillations close to the reservoirs. We demonstrate that anapproach based on time-dependent density functional theory copes with theseoscillations and predicts phase diagrams of bulk densities to a goodapproximation under arbitrary boundary-reservoir couplings. The minimum ormaximum current principles can be applied only for specific bulk-adaptedcouplings. We show that they generally fail to give the correct topology ofphase diagrams but can still be useful for getting insight into the mutualarrangement of different phases.

Classical Driven Transport in Open Systems with Particle Interactions and General Couplings to Reservoirs