Equilibrium sampling by re-weighting non-equilibrium simulation trajectories

TL;DR

This paper introduces RNED, a novel method extending reweighted ensemble dynamics to non-equilibrium simulations, enabling efficient equilibrium sampling from arbitrary initial distributions in complex systems.

Contribution

The paper presents RNED, a new approach that generalizes the Jarzynski equality for non-equilibrium trajectories starting from arbitrary initial states.

Findings

RNED accurately reproduces equilibrium distributions in toy and Lennard-Jones models.

RNED enhances sampling efficiency in complex conformational spaces.

The method successfully detects phase coexistence in simulated systems.

Abstract

With the traditional equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space in complex systems, which are separated into some metastable conformational regions by high free energy barriers. The applied non-equilibrium process in simulations could enhance the transitions among these conformational regions, and the associated non-equilibrium effects can be removed by employing the Jarzynski equality (JE), then the global equilibrium distribution can be reproduced. However, the original JE requires the initial distribution of the non-equilibrium process is equilibrium, which largely limits the application of the non-equilibrium method in equilibrium sampling. By extending the previous method, the reweighted ensemble dynamics (RED), which re-weights many equilibrium simulation trajectories from arbitrary initial distribution to reproduce the global equilibrium, to non-equilibrium simulations, we present a method, named as re-weighted non-equilibrium ensemble dynamics (RNED), to generalize the JE in the non-equilibrium trajectories started from an arbitrary initial distribution, thus provide an efficient method to reproduce the equilibrium distribution based on multiple independent (short) non-equilibrium trajectories. We have illustrated the validity of the RNED in a one-dimensional toy model and in a Lennard-Jones system to detect the liquid-solid phase coexistence.