As far as I know, there are quite a few questions (1, 2, 3) on Physics SE about the geometrical structure of thermodynamics.
I am really intrigued by this approach, but given that in equilibrium thermodynamics it does seem like overkill, I was wondering: Is there a well-established and useful application of contact geometry (or symplectic geometry on Riemannian manifolds, as suggested in some works) to non-equilibrium thermodynamics? By "useful and well-established," I mean an application that has been shown to predict or explain, in a clear and unambiguous way, non-equilibrium phenomena in real systems—phenomena that would otherwise be more easily approached using more conventional methods, such as Prigogine's Local Equilibrium Hypothesis or similar approaches.
