Characterizing the performance of heat rectifiers

A physical system connected to two thermal reservoirs at different temperatures is said to act as a heat rectifier when it is able to bias the heat current in a given direction, similarly to an electronic diode. We propose to quantify the performance of a heat rectifier by mapping out the trade-off between heat currents and rectification. By optimizing over the system's parameters, we obtain Pareto fronts, which can be efficiently computed using general coefficients of performance. This approach naturally highlights the fundamental trade-off between heat rectification and conduction, and allows for a meaningful comparison between different devices for heat rectification. We illustrate the practical relevance of these ideas on three minimal models for spin-boson nanoscale rectifiers, i.e., systems consisting of one or two interacting qubits coupled to bosonic reservoirs biased in temperature. Our results demonstrate the superiority of two strongly-interacting qubits for heat rectification.