发表机构
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China; School of Physical Science and Technology, Beijing University of Posts and Telecommunications; Institute of Theoretical Physics, Chinese Academy of Sciences; School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS; School of Physics, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院; 北京邮电大学物理科学与技术学院; 中国科学院理论物理研究所; 中国科学院大学杭州高等研究院基础物理与数学科学学院; 电子科技大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用变分自回归网络表征1-3维的SSEP、ASEP、TASEP的非平衡动力学，验证方法有效性，揭示各维度的动力学特性，建立统一表征框架。
AI 中文摘要
简单排斥过程（SEP）是非平衡输运的典型模型，但其在指数级大的构型空间上的时变联合分布所呈现的丰富动力学，一直被认为难以处理。本文利用变分自回归网络系统地表征一维到三维的对称简单排斥过程（SSEP）、不对称简单排斥过程（ASEP）和完全不对称简单排斥过程（TASEP）的非平衡动力学。我们首先通过重现一维SSEP的现有有限时间结果和二维SSEP的长时间张量网络结果验证该方法，随后提供一维和二维SSEP、ASEP、TASEP更丰富的有限时间动力学，以及三维的新有限时间分析。具体而言，在一维中，我们发现有限时间动力学活性图直接对应经典的TASEP三阶段稳态组织；在长时间极限下，边界和体效应分别控制从扩散输运到弹道输运过渡过程中的动力学 susceptibility。在二维中，我们建立了平均场方向密度准则，该准则得到了神经网络计算的支持，并表明长时间下的边界和体效应与一维的情况类似。在三维中，我们发现了SSEP活性-非活性相变的新有限时间标度关系，且揭示了相变点相对于系统大小的标度指数大致一致，这意味着无论维度如何，相变点渐近地由特征长度尺度（$s_c\sim L^{-2}$）控制。因此，本工作为表征代表性输运系统的非平衡动力学建立了统一框架。
英文摘要
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 $s_c\sim L^{-2}$, 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.
