Abstract
We study large deviations for the current of one-dimensional stochastic particle systems with periodic boundary conditions. Following a recent approach based on an earlier result by Jensen and Varadhan, we compare several candidates for atypical currents to travelling wave density profiles, which correspond to non-entropic weak solutions of the hyperbolic scaling limit of the process. We generalize previous results to partially asymmetric systems and systems with convex as well as concave current-density relations, including zero-range and inclusion processes. We provide predictions for the large deviation rate function covering the full range of current fluctuations using heuristic arguments, and support them by simulation results using cloning algorithms wherever they are computationally accessible. For partially asymmetric zero-range processes we identify an interesting dynamic phase transition between different strategies for atypical currents, which is of a generic nature and expected to apply to a large class of particle systems on a ring.
Highlights
Large deviations of dynamic observables in bulk-driven lattice gases have been a topic of major recent research interest
Strictly speaking, (54) is only an upper bound for the rate function, but we have good reason to believe that we considered all relevant strategies to realize current large deviations
We have demonstrated in the previous section and in [21] that the Jensen Varadhan approach for current large deviations, originally developed for the total ASEP (TASEP) [20], can be applied more generally to totally asymmetric stochastic particle systems with convex or concave currentdensity relations
Summary
Large deviations of dynamic observables in bulk-driven lattice gases have been a topic of major recent research interest. In recent work [21] this approach has been shown to apply for totally asymmetric ZRPs with concave current-density relation, where the validity can be limited by a crossover to condensed profiles in certain models constituting a dynamic phase transition. The point of this paper is to highlight the general applicability of the approach in [21] for general asymmetric particle systems with stationary product distributions This is illustrated by applications to the inclusion process (IP) with convex current-density relation, and ZRPs with a concave relation and partially asymmetric dynamics. We discuss such candidates for inclusion and partially asymmetric ZRPs, covering the full range of current deviations, and identifying interesting transitions between different types of optimal states This leads to a complete characterization of the rate function for both models, and we discuss how the generic nature of our approach can be applied in general particle systems.
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