Nonequilibrium candidate Monte Carlo: A new tool for efficient equilibrium simulation

TL;DR

This paper introduces Nonequilibrium Candidate Monte Carlo, a novel method that uses nonequilibrium dynamics to generate proposals with higher acceptance rates, significantly improving the efficiency of equilibrium simulations in complex systems.

Contribution

It presents a new class of Monte Carlo moves based on nonequilibrium dynamics that enhance sampling efficiency by increasing acceptance probabilities.

Findings

Increased acceptance rates in dense solvated systems.

Reduced structural correlation times in simulations.

Expanded capabilities for sampling from multiple thermodynamic states.

Abstract

Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. Here, we introduce a new class of moves based on nonequilibrium dynamics: candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution. The acceptance rule is similar to the Metropolis acceptance probability, but related to the nonequilibrium work rather than the instantaneous energy difference. Our method is applicable to sampling from both a single thermodynamic state or a mixture of thermodynamic states, and allows both coordinates and thermodynamic parameters to be driven in nonequilibrium proposals. While generating finite-time switching trajectories incurs an additional cost, driving some degrees of freedom while allowing others to evolve naturally can lead to large enhancements in acceptance probabilities, greatly reducing structural correlation times. Using nonequilibrium driven processes vastly expands the repertoire of useful Monte Carlo proposals in simulations of dense solvated systems.