Large deviations in boundary-driven systems: Numerical evaluation and effective large-scale behavior

TL;DR

This paper introduces a numerical method to evaluate rare event probabilities in boundary-driven diffusive systems, revealing that large-scale behavior can be effectively captured by a few modes or local equilibrium assumptions.

Contribution

It provides a novel numerical approach for calculating rare event probabilities and demonstrates how large-scale behavior can be simplified in boundary-driven diffusive systems.

Findings

Rare event probabilities can be computed numerically in 1D and 2D.

Large-scale configurations are described by few long wavelength modes.

Rapidly varying configurations can be approximated by local equilibrium.

Abstract

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we show that the probability density of a slowly varying configuration can be captured with a small number of long wave-length modes. For a configuration which varies rapidly in space this description can be complemented by a local equilibrium assumption.