Quantum Carnot Engine

The Frohlich pumped electric dipole membrane oscillations play a vital role in the microtubule models of consciousness. I noted in a question session that the pumping makes a population inversion corresponding to an effective negative temperature. The coupling of this negative temperature to surrounding positive temperature allows a quantum Carnot engine of greater than 100% efficiency. That is, heat flows from both the hot negative temperature bath and the cold positive temperature environment are converted to useful mechanical work. That is, the second law of thermodynamics says

Work Out/Hot Heat Flow = 1 - Cold Temp (K)/Hot Temp(K)

But quantum mechanics says that in this "laser" case

Cold Temp (K)/Hot Temp(K) < 0

Not only that, it is easy to have

Cold Temp (K)/Hot Temp(K) < < - 1

so that

Efficiency = Work Out/Hot Heat Flow >> 1