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

Carsten Hartmann, Christof Schuette, Wei Zhang

Published 2018-03-25, updated 2018-06-23Version 2

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.