Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions
Abstract
The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet its rich dynamics over an exponentially large configuration space remain notoriously intractable. Here, we leverage variational autoregressive networks to characterize the nonequilibrium dynamics of the symmetric (SSEP), asymmetric (ASEP), and totally asymmetric (TASEP) cases in one to three dimensions at any time. We validate the approach against established finite-time 1D and long-time 2D results for the SSEP, and further provide new results on dynamical activity, density fields and nonequilibrium phase transitions for 2D and 3D cases. In 2D, we give a directional-density criterion connecting the bulk-density organization to the 1D TASEP phase diagram, and reveal how boundary and bulk rates separately control the activity and susceptibility. In 3D, we provide the first finite-time characterization of the SSEP active-inactive phase transition, and uncover scaling relations over time. Across dimensions, the critical field follows a trend sc∼ L−2, suggesting tuning strategies by the characteristic diffusive length scale. Overall, this work establishes a unified neural-network framework for characterizing nonequilibrium dynamics of representative transport systems.
Related
- Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
- Exclusion vs Noncolliding Dynamics in Markov Processes
- Facilitated Exclusion Process in Higher Dimensions: Recurrent Structure and Transient Dynamics
- Dynamics for exclusion processes with random environments of particle jump rates
- Non-equilibrium fluctuations of gradient exclusion processes in dimension d≤ 3
BibTeX
@misc{liu2026nonequilibrium,
title = {{Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions}},
author = {Zhimao Liu and Jing Liu and Pan Zhang and Ying Tang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.25606},
eprint = {2608.25606},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25606},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions
AU - Zhimao Liu
AU - Jing Liu
AU - Pan Zhang
AU - Ying Tang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2608.25606
UR - https://arxiv.org/abs/2608.25606
AB - The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet its rich dynamics over an exponentially large configuration space remain notoriously intractable. Here, we leverage variational autoregressive networks to characterize the nonequilibrium dynamics of the symmetric (SSEP), asymmetric (ASEP), and totally asymmetric (TASEP) cases in one to three dimensions at any time. We validate the approach against established finite-time 1D and long-time 2D results for the SSEP, and further provide new results on dynamical activity, density fields and nonequilibrium phase transitions for 2D and 3D cases. In 2D, we give a directional-density criterion connecting the bulk-density organization to the 1D TASEP phase diagram, and reveal how boundary and bulk rates separately control the activity and susceptibility. In 3D, we provide the first finite-time characterization of the SSEP active-inactive phase transition, and uncover scaling relations over time. Across dimensions, the critical field follows a trend s_c∼ L^−2, suggesting tuning strategies by the characteristic diffusive length scale. Overall, this work establishes a unified neural-network framework for characterizing nonequilibrium dynamics of representative transport systems.
ER -