# Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics

arXiv: https://arxiv.org/abs/1503.02356 · HTML: https://mlsanity.com/paper/1503.02356/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2015.

## Built on by (most cited first, 3 of 3)

- [Forward-Backward Latent State Inference for Hidden Continuous-Time semi-Markov Chains](https://mlsanity.com/paper/2210.09058/) (2022)
- [Population Annealing as a Discrete-Time Schr"odinger Bridge](https://mlsanity.com/paper/2603.16056/) (2026)
- [Nonreversible Gauge Fields in Fokker--Planck Dynamics: Supersymmetric Hamiltonians and Learned Finite Forces](https://mlsanity.com/paper/2606.06412/) (2026)

## Abstract (arXiv)

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition-probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.