Memory Effect in Upper Bound of Heat Flux Induced by Quantum   Fluctuations
  Thermodynamic behaviors in a quantum Brownian motion coupled to a classical heat bath is studied. We then define a heat operator by generalizing the stochastic energetics and show the energy balance (first law) and the upper bound of the expectation value of the heat operator (second law). We further find that this upper bound depends on the memory effect induced by quantum fluctuations and hence the maximum extractable work can be qualitatively modified in quantum thermodynamics. 
T. Koide
quant-ph cond-mat.stat-mech hep-th