Accelerated Jarzynski Estimator with Deterministic Virtual Trajectories

TL;DR

This paper introduces a deterministic virtual trajectory method to accelerate the convergence of the Jarzynski estimator, improving partition function estimation in nonequilibrium statistical physics.

Contribution

The paper proposes a novel approach using deterministic trajectories under Hamiltonian dynamics to significantly speed up the Jarzynski estimator's convergence.

Findings

Achieves second-order acceleration over naive Langevin-based estimators

Demonstrates improved performance on multimodal distributions

Provides theoretical and numerical validation of the method

Abstract

The Jarzynski estimator is a powerful tool that uses nonequilibrium statistical physics to numerically obtain partition functions of probability distributions. The estimator reconstructs partition functions with trajectories of the simulated Langevin dynamics through the Jarzynski equality. However, the original estimator suffers from slow convergence because it depends on rare trajectories of stochastic dynamics. In this paper, we present a method to significantly accelerate the convergence by introducing deterministic virtual trajectories generated in augmented state space under the Hamiltonian dynamics. We theoretically show that our approach achieves second-order acceleration compared to a naive estimator with the Langevin dynamics and zero variance estimation on harmonic potentials. We also present numerical experiments on three multimodal distributions and a practical example where the proposed method outperforms the conventional method, and provide theoretical explanations.