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.
Highlights
The large deviation behaviour of dynamic observables has been a topic of major recent research interest in driven diffusive systems
We study lower current large deviations for general TAZRP with concave flux functions J (ρ), which can be realized by phase separated density profiles
These shocks can be stabelized by local changes in the dynamics and lead to rate functions which are independent of the system size, which have been studied before for the exclusion process
Summary
The large deviation behaviour of dynamic observables has been a topic of major recent research interest in driven diffusive systems. From the macroscopic point of view, one of the most powerful frameworks introduced in recent years is the macroscopic fluctuation theory (MFT) (see [14] and references therein), whose more general rigorous description is based on empirical flows [15,16] This is able to provide, as a result of a variational principle, the time evolution of the most likely density profile which typically gives rise to a given fluctuation. For non-entropic solutions the entropy production can provide the large deviation rate function for observing such a non-typical profile, if the correct thermodynamic entropy is used [20] This connection has been proved rigorously for the ASEP [21,22], giving rise to the so-called Jensen–Varadhan theory.
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