Maximum-power heat engines and refrigerators in the fast-driving regime

We study the optimization of performance arbitrary periodically driven thermal machines. Within assumption fast modulation driving parameters, we derive optimal cycle that universally maximizes extracted power heat engines, cooling refrigerators, and in general any linear combination currents. denote this solution as ``generalized Otto cycle'' since it shares basic structure with standard cycle, but is characterized by a greater number strokes. bound terms dimension Hilbert space system used working fluid. The generality these results allows for widespread range applications, such reducing computational complexity numerical approaches, or obtaining explicit form protocols when system-baths interactions are single thermalization scale. In case, compare thermodynamic collection optimally non-interacting interacting qubits. Remarkably, refrigerators qubits perform almost well ones, while engine case there many-body advantage both maximum power, efficiency at power. Additionally, illustrate our studying paradigmatic model qutrit-based engine. Our strictly hold semiclassical which no coherence generated driving, finally discuss non-commuting case.