Nonlocal correction to quantum heat flow

If you hit a quantum system, like a molecule, in one place the effect can be felt immediately far away, an effect we term "quantum work-at-a-distance." This is yet another example of a salient feature of quantum mechanics that always disturbed Albert Einstein, the non-local character of quantum states. We show that this nonlocal work must be subtracted from the total energy flow in order to correctly describe the flow of heat in quantum systems. Importantly, the heat dissipated by quantum machines including this correction is predicted to be orders of magnitude less than that predicted by the textbook heat current formula for certain classes of driving protocols. A new formula for entropy flow is postulated that includes the effects of both topological and non-topological quantum work. It is shown that failure to include the quantum work correction leads to paradoxical results for the thermodynamics of driven quantum systems.