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Nobumasa Ishida1, Yoshihiko Hasegawa1

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Summary
This summary is machine-generated.

This study accelerates the Jarzynski estimator for calculating partition functions. By using deterministic virtual trajectories, the new method significantly improves convergence speed over traditional Langevin dynamics.

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Area of Science:

  • Statistical Physics
  • Computational Physics
  • Numerical Analysis

Background:

  • The Jarzynski estimator, based on nonequilibrium statistical physics, is used to compute partition functions.
  • It reconstructs partition functions using the Jarzynski equality and Langevin dynamics.
  • The conventional estimator exhibits slow convergence due to reliance on rare stochastic trajectories.

Purpose of the Study:

  • To develop a method for accelerating the convergence of the Jarzynski estimator.
  • To improve the efficiency of numerical calculations of partition functions.

Main Methods:

  • Introduction of deterministic virtual trajectories within an augmented state space.
  • Utilizing Hamiltonian dynamics for generating these virtual trajectories.
  • Theoretical analysis and numerical experiments on multimodal distributions.

Main Results:

  • Achieved second-order acceleration compared to naive Langevin dynamics estimators.
  • Demonstrated zero variance estimation for harmonic potentials.
  • Numerical experiments confirmed superior performance against conventional methods.

Conclusions:

  • The proposed method significantly accelerates Jarzynski estimation convergence.
  • This approach offers a more efficient way to compute partition functions.
  • The technique shows promise for practical applications in statistical physics.