  Quantum coherence has been shown to impact the operational capabilities of
quantum systems performing thermodynamic tasks in a significant way, and yet
the possibility of genuine coherence-enhanced thermodynamic operation remains
unclear. Here we show that only the presence of energetic coherence --
coherence between levels with different energies -- in steady-state quantum
thermal machines can lead to genuine thermodynamic advantage. On the other
hand, engines showing coherence between degenerate levels, or subjected to
noise-induced coherence, are shown to be systematically outperformed by
classical stochastic engines using exactly the same set of (incoherent)
resources. We illustrate our results with three prototypical models of heat
engines and refrigerators and employ multi-objective optimization techniques to
characterize quantum-enhanced regimes in connection with the thermodynamic
uncertainty relation.
