Multitimescale method for approximating the path action relevant to non-equilibrium statistical physics

TL;DR

This paper introduces a multiscale MCMC method for efficiently approximating path actions in non-equilibrium statistical physics, allowing flexible endpoint sampling and improving numerical evaluation of path integrals.

Contribution

It adapts the multiscale MCMC approach to non-equilibrium physics, enabling endpoint flexibility and enhancing computational efficiency.

Findings

The method effectively approximates path actions in non-equilibrium systems.

It allows for variable endpoint sampling, which is novel in this context.

Numerical experiments demonstrate improved efficiency over traditional methods.

Abstract

A path integral formalism has been proposed recently for non-equilibrium statistical physics applications by the author. In this contribution we outline an efficient method for its numerical evaluation. The method used is based on the multiscale MCMC method of Ceperley and co-workers in quantum applications. A significant new feature of the method proposed is that the time endpoint is not fixed and indeed the endpoint sample is the principle object of interest.