Advancements in Milestoning II: Calculating Autocorrelation from Milestoning Data Using Stochastic Path Integrals in Milestone Space

TL;DR

This paper extends the Milestoning method to non-equilibrium systems by developing a stochastic path integral approach to calculate autocorrelation functions from Milestoning data, demonstrated on analytical and molecular systems.

Contribution

It introduces a new formalism for autocorrelation in Milestoning using stochastic path integrals, enabling non-equilibrium kinetic property calculations.

Findings

Analytical solution for harmonic oscillator autocorrelation.

Numerical results for two-well potential.

Application to molecular dynamics of alanine dipeptide.

Abstract

The Milestoning method has achieved great success in the calculation of equilibrium kinetic properties such as rate constants from molecular dynamics simulations. The goal of this work is to advance Milestoning into the realm of non-equilibrium statistical mechanics, in particular, the calculation of time correlation functions. In order to accomplish this, we introduce a novel methodology for obtaining flux through a given milestone configuration as a function of both time and initial configuration, and build upon it with a novel formalism describing autocorrelation for Brownian motion in a discrete configuration space. The method is then applied to three different test systems: a harmonic oscillator, which we solve analytically, a two well potential, which is solved numerically, and an atomistic molecular dynamics simulation of alanine dipeptide.