Lower current large deviations for zero-range processes on a ring

Abstract

We study lower large deviations for the current of totally asymmetric zero-range processes on a ring with concave current-density relation. We use an approach by Jensen and Varadhan which has previously been applied to exclusion processes, to realize current fluctuations by travelling wave density profiles corresponding to non-entropic weak solutions of the hyperbolic scaling limit of the process. We further establish a dynamic transition, where large deviations of the current below a certain value are no longer typically attained by non-entropic weak solutions, but by condensed profiles, where a non-zero fraction of all the particles accumulates on a single fixed lattice site. This leads to a general characterization of the rate function, which is illustrated by providing detailed results for four generic examples of jump rates, including constant rates, decreasing rates, unbounded sublinear rates and asymptotically linear rates. Our results on the dynamic transition are supported by numerical simulations using a cloning algorithm.

arXiv comment32 pages, 9 Figures

References in corpus (37)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• The large deviation approach to statistical mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Nonequilibrium Markov processes conditioned on large deviations
• Phase Transitions in one-dimensional nonequilibrium systems
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Simulating rare events in dynamical processes
• Sand as Maxwell's demon
• Condensation in the zero range process: stationary and dynamical properties
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Exact Current Statistics of the ASEP with Open Boundaries
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Current fluctuations in the zero-range process with open boundaries
• Wealth Condensation in Pareto Macro-Economies
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Current large deviations for driven periodic diffusions
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Breakdown of Gallavotti-Cohen symmetry for stochastic dynamics
• A simple stochastic model for the dynamics of condensation
• On the range of validity of the fluctuation theorem for stochastic Markovian dynamics
• Density profiles, dynamics, and condensation in the ZRP conditioned on an atypical current
• Thermodynamic Limit for the Invariant Measures in Supercritical Zero Range Processes
• Conformal invariance in driven diffusive systems at high currents
• Diffusions conditioned on occupation measures
• Condensation in stochastic particle systems with stationary product measures
• From urn models to zero-range processes: statics and dynamics
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Finite size effects and metastability in zero-range condensation
• Hydrodynamics of the zero-range process in the condensation regime
• Hydrodynamic Limit of mean zero condensing Zero Range Processes with sub-critical initial profiles
• A dynamical transition and metastability in a size-dependent zero-range process
• Finite-size effects on the dynamics of the zero-range process
• Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles

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• Dynamical Phase Transitions for Flows on Finite Graphs
• Current fluctuations for the boundary-driven zero-range process on graphs: microscopic versus macroscopic approach and a theory of non-reversible resistor-like networks