It wouldn't be a constant energy algorithm though, would it? For each successive optimization iteration, you would have to expend energy. Does that energy get put back with every rewind of the clock? If so, energy is also infinite.

I wonder what the time-energy-complexity trade-offs are?

As an aside, I would gladly pay someone to walk me through the math and physics sometime. (Any grad students in Atlanta are more than welcome to take me up on that offer... I might even try Skype.)