Thermodynamic Costs and Finite-Power Efficiency of Dephasing-Assisted Quantum Heat Engines

Abstract Quantum heat engines are commonly believed to achieve their optimal efficiency only when operated quasi-statically.
When running at finite power, however, they suffer effective friction due to the generation of coherences and transitions between energy eigenstates.
It was noted that it is possible to increase the power of a quantum heat engine using external control schemes or suitable dephasing noise.
Here, we investigate the thermodynamic cost associated with dephasing noise schemes using both numerical and analytical methods.
Our findings unveil that the observed gain in power is generally not free of thermodynamic costs, as it involves energy costs of the control fields or heat flows between thermal and dephasing baths.
These contributions must be duly accounted for when determining the engine's overall efficiency.
We identify suitable regimes in which, at a fixed effective dephasing rate, the heat leaked into the explicitly modelled dephasing bath can be made arbitrarily small, so that the efficiency at finite power approaches that of a quasi-statically operated Otto engine even when the dephasing environment is fully accounted for.