Probably it's possible to model catalytic contact mechanisms in chemistry taking place at boundaries. Take a 2-body system and see what happens when it bounces against a boundary, how the binding is stressed.
Besides vibrational modes using character theory (assume the edges as physical springs, see [Jam01]) could be useful.
Percolation, Ising models, phase transitions and field theory, multiple-length-scale phenomena and general statistical mechanics might be helpful, see for example [Ste04].
Terms like temperature used in combinatoric game theory (how much is a Go put worth) do come from thermodynamics, actually it's the (Eulerian) integrating denominator such that the resulting differential (the entropy) becomes exact, did u know? A game is like an experiment, it can burn slowly in a steady fashion, or it might develop 'hot' fighting.
We deal with concrete non-equilibrium dynamics here!