Finite-time performance of a cyclic two-dimensional quantum Ising heat engine

We discuss the limit cycle regime of a finite-time quantum Otto cycle with a frictionless two-dimensional anisotropic Ising model as the working fluid. From Onsager's exact equilibrium solution, we first find optimal parameters for the operational modes of work extraction and cooling for infinitely slow cycles. The equilibrium points in these optimal cycles correspond to different phases of the model, such that the nonequilibrium dynamics during the cycle bypasses the phase transition. Finite-time cycles allow for finite power extraction or cooling currents, but for such cycles, we point out that-already within the regime of weak system-reservoir coupling-energetic changes of the system during dissipative strokes may contain a significant portion of coupling and decoupling control work and should thus not be directly identified with heat. For ultrafast cycles, the required control work spoils performance, such that to maximize work extraction or cooling heat per cycle time, there is an optimal cycle duration. We also find that net-zero-energy transitions may lead to undesired reservoir heating.