Patterns of avoidance, adjacency, and association in complex systems design emerge from the system’s underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and spatial location). Understanding the physical–logical architecture interplay that gives rise to patterns of arrangement requires a quantitative approach that bridges both descriptions. Here, we show that statistical physics reveals patterns of avoidance, adjacency, and association across sets of complex, distributed system design solutions. Using an example arrangement problem and tensor network methods, we identify several phenomena in complex systems design, including placement symmetry breaking, propagating correlation, and emergent localization. Our approach generalizes straightforwardly to a broad range of complex systems design settings where it can provide a platform for investigating basic design phenomena.

复杂系统设计中的回避、邻接和关联模式来自系统底层逻辑架构（组件之间的功能关系）和物理架构（组件物理属性和空间位置）。理解产生排列模式的物理-逻辑架构相互作用需要一种量化方法来弥合这两种描述。在这里，我们展示了统计物理学揭示了复杂的分布式系统设计解决方案集之间的回避、邻接和关联模式。使用示例排列问题和张量网络方法，我们确定了复杂系统设计中的几种现象，包括放置对称性破坏、传播相关性和紧急定位。