Path integral analysis of Jarzynski's equality: Analytical results

TL;DR

This paper uses path integral methods to analyze nonequilibrium work theorems in Brownian dynamics, deriving equations for dominant trajectories, and validating Jarzynski's equality in specific harmonic systems.

Contribution

It introduces an analytical path integral framework to study work theorems, providing explicit solutions for harmonic systems and confirming Jarzynski's equality.

Findings

Derived equations of motion for dominant trajectories.

Evaluated work-weighted propagators for harmonic systems.

Validated Jarzynski's equality analytically.

Abstract

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski's equality.