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We study the finite-time effects in a quantum Otto cycle where a collectivespin system is used as the working fluid. Starting from a simple one-qubitsystem we analyze the transition to the limit cycle in the case of afinite-time thermalization. If the system consists of a large sample ofindependent qubits interacting coherently with the heat bath, the superradiantequilibration is observed. We show that this phenomenon can boost the power ofthe engine. Mutual interaction of qubits in the working fluid is modeled by theLipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantumphase transitions for the ground and excited states may have a strong negativeeffect on the performance of the machine. Reversely, by analyzing the workoutput we can distinguish between the operational regimes with and without aphase transition.

Collective performance of a finite-time quantum Otto cycle