Researchers have compared two prominent theoretical approaches for describing heat transport by thermal microwave photons in quantum circuits, finding that both models produce identical results under certain conditions. The models analyzed are the weak-coupling Lindblad master equation and a circuit model incorporating thermal Johnson-Nyquist noise. This agreement validates the application of the Lindblad equation for analyzing heat transport in complex quantum circuits, including those with qubits or nonlinear resonators.

The first model, based on the weak-coupling Lindblad master equation, determines transition rates via Fermi's golden rule, driven by thermal dissipation sources. The second approach, the circuit model, describes how thermal Johnson-Nyquist noise generated by dissipative elements induces currents and, consequently, Joule power in other parts of the circuit. This latter leads to a Landauer-type expression for heat transport, where the transmission coefficient is proportional to the circuit's transconductance.

The comparison revealed that, for a linear circuit in the weak-coupling limit, both models yield identical analytical expressions for the transported power. This finding was demonstrated in an archetypal circuit where a cavity mediates heat transport between two thermal baths. This analysis not only provides a quantitative assessment of the range of validity of the weak-coupling assumption in a circuit but also reinforces confidence in the applicability of the weak-coupling Lindblad model for more complex quantum systems.