  We introduce a simple nonequilibrium model for a driven diffusive system with
nonconservative reaction kinetics which exhibits ergodicity breaking and
hysteresis in one dimension. These phenomena can be understood through a
description of the dominant stochastic many-body dynamics in terms of an
equilibrium single-particle problem, viz. the random motion of a shock in an
effective potential. This picture also leads to the exact phase diagram of the
system and suggests a new generic mechanism for "freezing by heating".
