Occurrence of discontinuities in the performance of finite-time quantum   Otto cycles
  We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency. 
Yuanjian Zheng, Peter H\"anggi, Dario Poletti
cond-mat.stat-mech cond-mat.quant-gas quant-ph