Typical challenges in the design of modern integrated systems involve selecting a good layout for heterogeneous components, while trying to fulfill several different design objectives at the same time. Historically, such challenges have been cast into different mathematical forms, most commonly optimization problems. The last 20 years have seen a gradual shift to view large design problems instead as constraint-satisfaction problems and to look for sets of feasible solutions. In this work we cast design problems in terms of maximal-entropy statistical physics problems. Doing so doesn't just let us combine the best of the two previous approaches, but also allows us to tap into a rich arsenal of physics techniques, from studying the problem at any desired scale via coarse graining, to the characterization of architecture class robustness via materials physics language. We demonstrate the power of this approach on several arrangement problems from Naval Engineering, but this paradigm is applicable to a broad range of other design problems.