Dynamical Theory of Steady State Selection in Open Driven Diffusive Systems

The stationary states of one-dimensional driven diffusive systems, connected to boundary reservoirs with fixed particle density are shown to be selected by an extremal principle for the macroscopic current. Given the current one obtains the exact first- and second-order non-equilibrium phase transition lines for the bulk density as a function of the boundary densities. The basic dynamical mechanism behind the extremal principle is an intriguing generic interplay between the motion of shocks and localized perturbations.