Abstract
We study the relationship between quantum synchronization and the thermodynamic performance of a four-level near-degenerate extension of the Scovil-Schulz Dubois thermal maser. We show how the existence of interacting coherences can potentially modify the relationship between synchronization and the coherent power output of such a maser. In particular, the cooperation and competition between interacting coherences, causes the coherent heat and efficiency to be bounded by the synchronization measure in addition to the well-studied power synchronization bound. Overall, our results highlight the role of quantum synchronization in the working of a thermal machine.