[aifer4]

These results probably would not hold in the same form for a quantum system. By a quantum system, I mean a system where the decoherence time is on the order of the other timescales present in the system (e.g. the correlation time). In fact, it would be much more difficult to engineer such a system, and we would not want one for this purpose; the results rely on convergence to a classical canonical equilibrium distribution, which has to be generalized in the quantum case, meaning it may not have the properties we want. Also, we would have to deal with the measurement backaction on the system in the quantum limit, which we definitely don't want. In the classical limit, where the energy is much larger than Planck's constant divided by the timescale of the system, this is not an issue. One more thing: our algorithms use continuous measurement of the system. For a quantum system, due to the quantum Zeno effect, the system would be effectively "frozen", so we would definitely not sample the full distribution.