Szilard-like quantum heat engines in finite time

In a quantum Szilard engine, a contribution towards the net extracted work originates from the re-orientation of the energy-spectrum during insertion and removal of a potential barrier. In more practical experimental situations, the process of insertion or removal of the barrier is not adiabatic. Using numerical simulations, we explore the process of insertion of the potential barrier at various rates, taking the interaction with a thermal bath into consideration and the corresponding work required is calculated in the process. We show that in the case of very slow insertion, this work asymptotically approaches the adiabatic limit. We also discuss Szilard and Stirling-like quantum heat engines operating in finite-time using this understanding.