Extreme current fluctuations of boundary-driven systems in the large-N limit

TL;DR

This paper introduces large-N models for boundary-driven diffusive systems, revealing that hydrodynamic theories can accurately predict current fluctuations even beyond their traditional limits, with implications for understanding large deviations.

Contribution

The study provides exact derivations of current large deviation functions for finite systems and demonstrates the conditions under which hydrodynamic predictions remain valid for large currents.

Findings

Hydrodynamic theory accurately predicts large current fluctuations in certain models.

Symmetric inclusion processes follow hydrodynamic predictions for arbitrarily large currents.

Hydrodynamic theory's applicability depends on the unboundedness of the mobility coefficient.

Abstract

Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this question in detail, we introduce a class of large-N models of one-dimensional boundary-driven diffusive systems, whose current large deviation functions are exactly derivable for any finite number of sites. Surprisingly, we find that for some systems the predictions of the hydrodynamic theory may hold well beyond their naive regime of validity. Specifically, we show that, while a symmetric partial exclusion process exhibits non-hydrodynamic behaviors sufficiently far beyond the naive hydrodynamic regime, a symmetric inclusion process is well described by the hydrodynamic theory for arbitrarily large currents. We conjecture, and verify for zero-range processes, that the hydrodynamic theory captures the statistics of arbitrarily large currents for all models where the mobility coefficient as a function of density is unbounded from above. In addition, for the large-N models, we prove the additivity principle under the assumption that the large deviation function has no discontinuous transitions.