Multi-stage quantum absorption heat pumps

It is well known that heat pumps, while being all limited by the same basic thermodynamic laws, may find realization on systems as "small" and "quantum" as a three-level maser. In order to quantitatively assess how the performance of these devices scales with their size, we design generalized $N$-dimensional ideal heat pumps by merging $N-2$ elementary three-level stages. We set them to operate in the absorption chiller mode between given hot and cold baths, and study their maximum achievable cooling power and the corresponding efficiency as a function of $N$. While the efficiency at maximum power is roughly size-independent, the power itself slightly increases with the dimension, quickly saturating to a constant. Thus, interestingly, scaling up autonomous quantum heat pumps does not render a significant enhancement beyond the optimal double-stage configuration.