I'm pretty sure the actually difficult (i.e.: not handled by the heuristics TSP solvers use in practice) examples for TSP are impractical to convert to a physic

I'm pretty sure the actually difficult (i.e.: not handled by the heuristics TSP solvers use in practice) examples for TSP are impractical to convert to a physical object, and I'm not sure that physics would actually do a good job with them. Remember, it's the principal of _stationary_ action, not _least_ action, so it's basically a greedy search.