Hysteresis in one-dimensional reaction-diffusion systems.

We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics in one dimension. The steady state exhibits a phase with broken ergodicity and hysteresis which has no analog in systems investigated previously. We identify the main dynamical mode, viz., the random motion of a shock in an effective potential, which provides a unified framework for understanding phase coexistence as well as ergodicity breaking. This picture also leads to the exact phase diagram of the system.