Broken Ergodicity in Driven One-Dimensional Particle Systems with Short-Range Interaction
2006, v.12, №2, 309-332
We present a one-dimensional nonequilibrium model for a driven diffusive system which has local interactions and slow nonconservative reaction kinetics. Monte-Carlo simulations suggest that in the thermodynamic limit the steady state exhibits a phase with broken ergodicity. We propose a hydrodynamic equation for the coarse-grained density (under Eulerian scaling), augmented by a prescription how to treat shock and boundary discontinuities, respectively. This conjecture can be readily generalized to other weakly nonconservative driven diffusive systems and is supported by a heuristic identification of the main dynamical mode that governs the microscopic dynamics, viz. the random motion of a shock in an self-organized effective potential. This picture leads to the exact phase diagram of the system and suggests a novel and mathematically tractable mechanism for "freezing by heating".
Keywords: broken ergodicity,nonequilibrium phase transition,asymmetric simple exclusion process,biological transport processes