Langevin dynamics neglecting detailed balance condition

TL;DR

This paper introduces a modified Langevin dynamics approach that violates detailed balance to accelerate convergence to the desired distribution, demonstrated by faster relaxation and shorter correlation times in simulations.

Contribution

It formulates a Langevin dynamics without detailed balance, leading to improved relaxation speed and efficiency in reaching target distributions.

Findings

Faster convergence to the Gibbs-Boltzmann distribution.

Shorter correlation times in numerical simulations.

Enhanced efficiency demonstrated with biased event sampling.

Abstract

An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann distribution involve numerical simulations under the detailed balance condition. In contrast, in the present study we formulate the Langevin dynamics, for which the corresponding Fokker-Planck operator includes an asymmetric component violating the detailed balance condition. This leads to shifts in the eigenvalues and results in the acceleration of the relaxation toward the steady state. The numerical implementation demonstrates faster convergence and shorter correlation time, and the technique of biased event sampling, Nemoto-Sasa theory, further highlights the efficacy of our method.