Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions
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The paper applies variational autoregressive networks to study the time‑dependent joint distribution of the simple exclusion process (SEP) across symmetric, asymmetric, and totally asymmetric variants in one, two, and three dimensions. It reproduces known finite‑time results in 1D and 2D, provides new finite‑time dynamics for all three models, and uncovers scaling relations for the active‑inactive phase transition in 3D, showing a dimension‑independent characteristic length scale. The work offers a unified computational framework for probing nonequilibrium transport dynamics in high‑dimensional configuration spaces.
The paper demonstrates that long‑time stochastic dynamics can be predicted using generative diffusion models trained only on configuration pairs separated by a short, fixed time lag, without requiring the underlying equations of motion. Applied to two‑dimensional Model B and driven colloids in a periodic optical potential, the learned transition kernels accurately reproduce dynamic critical scaling, self‑similar coarsening, and experimental observables such as particle current and mean passage time, even on larger lattices and unseen initial conditions. This shows that short‑time observations contain sufficient information to forecast emergent non‑equilibrium behavior over extended periods.
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