Reductions of hard problems to physical models I am looking for examples of hard problems (in NP or harder) from computer science which can be reduced to models of physical processes.

For example, max-2-sat can be reduced to energy minimization in an Ising model.  I would like to find more examples of this type of reduction.
Counting constraint-satisfaction problems (#CSP), evaluating partition functions of many physical models, as well as many topics in classically simulating quantum states/circuits, are all fundamentally contracting tensor networks, which is a #P-complete problem. For a good overview see the following papers: 

Itai Arad, Zeph Landau, Quantum computation and the evaluation of tensor networks

Cai, Lu, Xia Holographic Algorithms with Matchgates Capture Precisely Tractable Planar #CSP

See especially the introduction of the latter for the connection to physical models.