I was interested in the physical-system analogy and use of the Hamiltonian to explore probability space. Since hamiltonian systems are conservative (no dissipative losses), they often fall into simple, periodic orbits. Sometimes though they have quite complex, or even chaotic orbits, depending on initial conditions. I presume one would restart this several times, using a variety of initial conditions? This seems like a neat idea for exploring a manifold! I wonder if it could be adapted for other purposes....?