General theory for thermal and nonthermal quantum linear engines

We present the exact theory of quantum engines whose working medium is a network of driven oscillators performing an arbitrary cyclic process while coupled to thermal and nonthermal reservoirs. We show that when coupled to a single reservoir work cannot be extracted unless there is population inversion, and prove that the ratio between the heat flowing out and into the working medium cannot be arbitrarily small, satisfying a form of Clausius inequality. We use such identity to prove that the efficiency of linear quantum engines satisfies a generalized bound, which coincides with the Carnot limit for thermal reservoirs. The previous results enable us to estimate the cost of preparing nonthermal reservoirs, which, if available, could be used to violate the Carnot limit.