We introduce a universal scheme to divide the power output of a periodicallydriven quantum heat engine into a classical contribution and one stemmingsolely from quantum coherence. Specializing to Lindblad-dynamics and smalldriving amplitudes, we derive general upper bounds on both, the coherent andthe total power. These constraints imply that, in the linear-response regime,coherence inevitably leads to power losses. To illustrate our general analysis,we explicitly work out the experimentally relevant example of a single-qubitengine.
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