Hysteresis in one-dimensional reaction-diffusion systems

Abstract

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".

arXiv comment4 Pages, 5 figures

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• Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system
• Totally asymmetric exclusion process with long-range hopping
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• Ergodicity breaking in one-dimensional reaction-diffusion systems
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• On-site residence time in a driven diffusive system: violation and recovery of mean-field
• Duality and phase diagram of one dimensional transport
• Microtubule length dependence of motor traffic in cells
• Exclusion model of mRNA translation with collision-induced ribosome drop-off
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• Fleming-Viot particle system driven by a random walk on $\mathbb{N}$
• Effective ergodicity breaking in an exclusion process with varying system length