Steady-state selection in driven diffusive systems with open boundaries

We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic current irrespective of the local dynamics. In particular, we predict a minimal current phase for systems with local minimum in the current--density relation. This phase is explained by a dynamical phenomenon, the branching and coalescence of shocks, Monte-Carlo simulations confirm the theoretical scenario.