Internal components of continuous quantum thermal machines.
The dynamics of continuous quantum machines weakly coupled to thermal reservoirs is described by master equations when the bath temperatures are high enough. If, in addition, the bare frequency gaps are much larger than the thermal couplings, the steady state or limit cycle of the device coincides with the stationary solution of a set of balance equations. This solution can be analyzed by using Graph Theory. Within this framework, the balance equations are represented by a graph. We employ a circuit decomposition of this graph to calculate and, most importantly, interpret the stationary thermodynamic properties of different continuous devices. We show that each circuit can be associated with a thermodynamically consistent mechanism. This follows from the consistency of the corresponding master equations with the Laws of Thermodynamics for a proper definition of the energy currents. As a consequence, these circuits can be thought of as internal components of the corresponding machine. Thus, the overall steady state functioning of the device is the result of the contributions of its internal components and the interplay between them. We study two types of continuous devices. On one hand, we analyze ab- sorption machines including only thermal baths. We show here that not only the total number of constituents circuits affects the device performance, but also the specific structure of the graph containing these circuits. Crucially, we find that the device connectivity has a major role in the design of optimal absorption machines. On the other hand, we consider periodically driven devices with a cyclic pattern of transitions. These machines are connected to thermal baths and also to a sinusoidal laser field. We study both the strong and the weak driving limits by using Global and Local master equa- tions respectively. We compare these approaches with the Redfield master equation. A circuit decomposition can be used to describe the stationary thermodynamic quantities in both limits. Interestingly, given an arbitrary basis, the device needs coherences to operate in the weak driving limit. How- ever, an incoherent stochastic-thermodynamic model may replicate the same stationary functioning. We conclude that the steady state thermodynamic operation in all the models under consideration can be described without invoking any quantum feature. Along these lines, the graph approach may be useful for identify- ing genuinely quantum effects in other continuous machines. For example, devices with non-cyclic pattern of transitions and degenerate states.