# Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions

arXiv: https://arxiv.org/abs/2608.25606 · HTML: https://mlsanity.com/paper/2608.25606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 90 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [A reinforcement learning approach to rare trajectory sampling](https://mlsanity.com/paper/2005.12890/) (2020)
- [Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects](https://mlsanity.com/paper/2410.14466/) (2024)
- [Neural-network solutions to stochastic reaction networks](https://mlsanity.com/paper/2210.01169/) (2022)
- [Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz](https://mlsanity.com/paper/2011.08657/) (2020)
- [WeightFlow: Learning Stochastic Dynamics via Evolving Weight of Neural Network](https://mlsanity.com/paper/2508.00451/) (2025)
- [Quantum Flow Matching](https://mlsanity.com/paper/2508.12413/) (2025)
- [Tracking large chemical reaction networks and rare events by neural networks](https://mlsanity.com/paper/2512.10309/) (2025)
- [Scalable Physics-Inspired Transformers for Spin Glasses](https://mlsanity.com/paper/2606.22984/) (2026)

## Abstract (arXiv)

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.