Kinetic Flat-Histogram Simulations of Non-Equilibrium Stochastic Processes with Continuous and Discontinuous Phase Transitions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908854336356352 |
|---|---|
| author | Alencar, L. M. C. Alves, T. F. A. Alves, G. A. Lima, F. W. S. Macedo-Filho, A. Ferreira, R. S. |
| author_facet | Alencar, L. M. C. Alves, T. F. A. Alves, G. A. Lima, F. W. S. Macedo-Filho, A. Ferreira, R. S. |
| contents | As far as we know, there is no flat-histogram algorithm to sample the stationary distribution of non-equilibrium stochastic processes. The present work addresses this gap by introducing a generalization of the Wang-Landau algorithm, applied to non-equilibrium stochastic processes with local transitions. The main idea is to sample macroscopic states using a kinetic Monte Carlo algorithm to generate trial moves, which are accepted or rejected with a probability that depends inversely on the stationary distribution. The stationary distribution is refined through the simulation by a modification factor, leading to convergence toward the true stationary distribution. A visitation histogram is also accumulated, and the modification factor is updated when the histogram satisfies a flatness condition. The stationary distribution is obtained in the limit where the modification factor reaches a threshold value close to unity. To test the algorithm, we compare simulation results for several stochastic processes with theoretically known behavior. In addition, results from the kinetic flat-histogram algorithm are compared with standard exact stochastic simulations. We show that the kinetic flat-histogram algorithm can be applied to phase transitions in stochastic processes with bistability, which describe a wide range of phenomena such as epidemic spreading, population growth, chemical reactions, and consensus formation. With some adaptations, the kinetic flat-histogram algorithm can also be applied to stochastic models on lattices and complex networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kinetic Flat-Histogram Simulations of Non-Equilibrium Stochastic Processes with Continuous and Discontinuous Phase Transitions Alencar, L. M. C. Alves, T. F. A. Alves, G. A. Lima, F. W. S. Macedo-Filho, A. Ferreira, R. S. Statistical Mechanics As far as we know, there is no flat-histogram algorithm to sample the stationary distribution of non-equilibrium stochastic processes. The present work addresses this gap by introducing a generalization of the Wang-Landau algorithm, applied to non-equilibrium stochastic processes with local transitions. The main idea is to sample macroscopic states using a kinetic Monte Carlo algorithm to generate trial moves, which are accepted or rejected with a probability that depends inversely on the stationary distribution. The stationary distribution is refined through the simulation by a modification factor, leading to convergence toward the true stationary distribution. A visitation histogram is also accumulated, and the modification factor is updated when the histogram satisfies a flatness condition. The stationary distribution is obtained in the limit where the modification factor reaches a threshold value close to unity. To test the algorithm, we compare simulation results for several stochastic processes with theoretically known behavior. In addition, results from the kinetic flat-histogram algorithm are compared with standard exact stochastic simulations. We show that the kinetic flat-histogram algorithm can be applied to phase transitions in stochastic processes with bistability, which describe a wide range of phenomena such as epidemic spreading, population growth, chemical reactions, and consensus formation. With some adaptations, the kinetic flat-histogram algorithm can also be applied to stochastic models on lattices and complex networks. |
| title | Kinetic Flat-Histogram Simulations of Non-Equilibrium Stochastic Processes with Continuous and Discontinuous Phase Transitions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2505.20651 |