Importance sampling large deviations in nonequilibrium steady states. I

TL;DR

This paper evaluates trajectory-based sampling methods for computing large deviation functions in nonequilibrium steady states, highlighting convergence issues and proposing improvements for efficiency.

Contribution

It compares different sampling techniques, demonstrates their limitations, and suggests guiding functions to enhance the accuracy of large deviation function estimation.

Findings

Transition path sampling and diffusion Monte Carlo suffer from exponential correlation divergence.

Guiding functions improve the efficiency of trajectory sampling algorithms.

The methods are illustrated on models including a biased Brownian walker and driven lattice gas.

Abstract

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult, because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.