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We consider a collision model representation of nonequilibrium dynamics for an externally driven open quantum system. Specifically we investigate the nondemolition quasiprobability distributions (QPDFs) of work and heat in both Markovian and non-Markovian regimes. In this model, work and heat correspond to different evolution processes, and their contributions can be distinguished. For the system state with initial coherence, in both Markovian and non-Markovian regimes, negative quasiprobabilities at half of the energy gap of the system for work and the variation of internal energy appear, which is considered to be a witness of the quantumness of the system. We also find that when the external driving speed slows down, the quantumness of the system is weakened, and when the driving speed is slow enough, the negative quasiprobability will disappear and the results of the QPDF coincide with those of the two-measurement protocol. Most importantly, we find that non-Markovianity can enhance the quantumness of the system.
Li et al. (Fri,) studied this question.