Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization

TL;DR

This paper introduces a variance minimization approach to construct guiding distribution functions for nonequilibrium systems, significantly improving Monte Carlo estimations of large deviation functions by reducing variance growth.

Contribution

The authors develop a novel variance minimization technique to optimize guiding distribution functions, enhancing the efficiency of Monte Carlo methods in nonequilibrium systems.

Findings

Optimized GDFs improve efficiency in driven diffusive systems.

Correlator product state ansatz captures phase transition features.

Method extends tools for studying nonequilibrium properties.

Abstract

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D WASEP. We show that with modest resources we can capture the features of the susceptibility in large systems that marks the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.