Avoidance, Adjacency, and Association: Statistical Mechanics Insight into Distributed Systems Design*

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.