Constructing systems that exhibit timescales much longer than those of the underlying components, as well as emergent dynamical and collective behavior, is a key goal in fields such as synthetic biology and materials self-assembly. Inspiration often comes from living systems, in which robust global behavior prevails despite the stochasticity of the underlying processes. Here, we present two-dimensional stochastic networks that consist of minimal motifs representing out-of-equilibrium cycles at the molecular scale and support chiral edge currents in configuration space. These currents arise in the topological phase because of the bulk-boundary correspondence and dominate the system dynamics in the steady state, further proving robust to defects or blockages. We demonstrate the topological properties of these networks and their uniquely non-Hermitian features such as exceptional points and vorticity, while characterizing the edge-state localization. As these emergent edge currents are associated with macroscopic timescales and length scales, simply tuning a small number of parameters enables varied dynamical phenomena, including a global clock, dynamical growth and shrinkage, and synchronization. Our construction provides a novel topological formalism for stochastic systems and fresh insights into non-Hermitian physics, paving the way for the prediction of robust dynamical states in new classical and quantum platforms.

中文翻译：

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拓扑保护随机系统中的手征边缘电流

构建时间尺度比底层组件长得多的系统，以及涌现的动态和集体行为，是合成生物学和材料自组装等领域的关键目标。灵感通常来自生命系统，尽管潜在过程具有随机性，但在该系统中，强大的全球行为依然盛行。在这里，我们提出了二维随机网络，该网络由代表分子尺度上的失衡循环的最小基序组成，并支持配置空间中的手性边缘电流。由于体边界对应，这些电流在拓扑阶段出现，并在稳态下主导系统动力学，进一步证明对缺陷或阻塞的鲁棒性。我们展示了这些网络的拓扑特性及其独特的非厄米特征，例如异常点和涡度，同时表征了边缘状态定位。由于这些涌现的边缘电流与宏观时间尺度和长度尺度相关，因此只需调整少量参数即可实现各种动态现象，包括全局时钟、动态增长和收缩以及同步。我们的构建为随机系统提供了一种新颖的拓扑形式，并为非厄米物理学提供了新的见解，为在新的经典和量子平台中预测鲁棒动力学铺平了道路。由于这些涌现的边缘电流与宏观时间尺度和长度尺度相关，因此只需调整少量参数即可实现各种动态现象，包括全局时钟、动态增长和收缩以及同步。我们的构建为随机系统提供了一种新颖的拓扑形式，并为非厄米物理学提供了新的见解，为在新的经典和量子平台中预测鲁棒动力学铺平了道路。由于这些涌现的边缘电流与宏观时间尺度和长度尺度相关，因此只需调整少量参数即可实现各种动态现象，包括全局时钟、动态增长和收缩以及同步。我们的构建为随机系统提供了一种新的拓扑形式，并为非厄米物理学提供了新的见解，为在新的经典和量子平台中预测鲁棒动力学铺平了道路。