Optimal work of quantum Szilard engine
  We have found the optimal condition of the work performed by the quantum Szilard engine (SZE) containing multi-particles. Usually the optimal work of a cyclic engine is achieved when the whole thermodynamic process is reversible. Although the quantum SZE inherently contains an irreversible process, we can still define effectively reversible protocol based upon the force of time-forward and time-backward processes. 
Hee Joon Jeon and Sang Wook Kim
quant-ph cond-mat.stat-mech