Sure, but this is still a statistical approach, assuming no knowledge of each individual atom or molecule, as one would need in attempting to reverse a gas diffusion process, as I was hypothesising. So in your terms, this approach has already "lost" the information. What I was driving at is that the deterministic simulation may be impossible for QM reasons, because of how the distribution among states actually arises through QM processes.
But again, what about discussion with people in other departments at your institution? Or are you retired already?
Not retired, but I don't get over to that side of campus much. Probably I should.