  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 simulated Langevin dynamics through the Jarzynski equality. However, the
original estimator suffers from its 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 Hamiltonian dynamics. We
theoretically show that our approach achieves second-order acceleration
compared to a naive estimator with Langevin dynamics and zero variance
estimation on harmonic potentials. Moreover, we conduct numerical experiments
on three multimodal distributions where the proposed method outperforms the
conventional method, and provide theoretical explanations.
