John Baez introduces a notion of “quantropy” which is supposed to be a quantum-dynamical analogue to entropy in statistical mechanics.
“But wait,” you say, “there’s already a perfectly good notion of entropy in quantum mechanics: von Neumann entropy!”
Yes, I reply, but that’s still statistical mechanics; quantum statistics. Baez’s analogy is between thermodynamics and the path integral formulation of quantum dynamics.
“Is that really a robust analogy?” you ask.
I’ll need a better night’s sleep before I can give you an answer on that, I reply.