We study the problem of performance optimization of generic driven (quantum) thermal machines that can be put in contact with multiple thermal reservoirs. The dynamical problem is simplified by using techniques based on the separation between the characteristic timescale of the driving and the relaxation timescale of the working fluid.
In the regime of slow-driving we give general principles for the maximization of power output at given (small) dissipation [2], and we solve completely the case of a Carnot engine at any efficiency [1], finding that the best performance is intimately connected to the heat capacity of the working fluid, which opens the possibility of realizing engines that reach Carnot efficiency at finite power in the thermodynamic limit.
In the opposite regime of fast-driving we derive the optimal strategy for power maximization, which ultimately consists in a generalized fast Otto cycle made by a number of quenches that can be upper bounded based on the working fluid dimension and machine type [3].

[1] Abiuso, P.; Perarnau-Llobet, M. (2020) Physical Review Letters, 124(11), 110606.
[2] Abiuso, P.; J. D. Miller, H.; Perarnau-Llobet, M.; Scandi, M. Entropy (2020), 22, 1076.
[3] Cavina, V.; Erdman, P.A.; Abiuso, P.; Tolomeo L.; Giovannetti, V. arXiv 2010.00586