  We study the finite-time effects in a quantum Otto cycle where a collective
spin system is used as the working fluid. Starting from a simple one-qubit
system we analyze the transition to the limit cycle in the case of a
finite-time thermalization. If the system consists of a large sample of
independent qubits interacting coherently with the heat bath, the superradiant
equilibration is observed. We show that this phenomenon can boost the power of
the engine. Mutual interaction of qubits in the working fluid is modeled by the
Lipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantum
phase transitions for the ground and excited states may have a strong negative
effect on the performance of the machine. Reversely, by analyzing the work
output we can distinguish between the operational regimes with and without a
phase transition.
