Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms

TL;DR

This paper provides a mathematical review and generalization of Jarzynski's equality and fluctuation theorems for diffusion processes, and explores variance reduction techniques like importance sampling for computing free energy differences.

Contribution

It offers a rigorous mathematical analysis of nonequilibrium theorems and introduces variance reduction algorithms for improved numerical computation of free energy.

Findings

Generalized fluctuation theorems for diffusion processes

Mathematical framework for Jarzynski's equality

Effective importance sampling algorithms for free energy calculation

Abstract

In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality.