Relation between topology and heat currents in multilevel absorption machines

The steady state heat currents of continuous absorption machines can be decomposed into thermodynamically consistent contributions, each of them associated with a circuit in the graph representing the master equation of the thermal device. We employ this tool to study the functioning of absorption refrigerators and heat transformers with an increasing number of active levels. Interestingly, such an analysis is independent of the particular physical implementation (classical or quantum) of the device. We provide new insights into the understanding of scaling up thermal devices concerning both the performance and the magnitude of the heat currents. Indeed, it is shown that the performance of a multilevel machine is smaller or equal than the corresponding to the largest circuit contribution. Besides, the magnitude of the heat currents is well-described by a purely topological parameter which in general increases with the connectivity of the graph. Therefore, we conclude that for a fixed number of levels, the best of all different constructions of absorption machines is the one whose associated graph is as connected as possible, with the condition that the performance of all the contributing circuits is equal.