I love so much the “Transparency is better than trust” idea that I put it on the top of my page. Like I did for em, I want to announce the start of a new draft where is formulated a general mathematical treatment which aims to solve a growing collection of coincidences between dissipation as treated in convex analysis and the hamiltonian formalism.
This form of dissipation function, discovered by De Saxce, called by him “bipotential”, shares some very intriguing features with hamiltonians. In past articles about the mathematical treatment of bipotentials these features were noted as curiosities (for example the ressemblance between convex lagrangian covers (remark 6.1 here) and lagrangian fibrations from quantization).
But with formalism from the draft, which extends the one from arXiv.1807.10480, indeed dissipation will be treated with the same mathematical formalism as hamiltonians (from a stochastic point of view).
I don’t say that dissipation is a sort of hamiltonian, mind you, I say that once again nature likes to repeat a winning pattern, in a different context.
So follow that link from time to time, because I am going to update it until it reaches the final form.