Abstract
Finite-time cycle period for a quantum Otto machine implies that either an adiabatic stroke or an isochoric process proceeds in finite time duration. The quantum Otto refrigerators under consideration consist of two adiabatic strokes, where the system (isolated from the heat reservoir) undergoes finite-time unitary transformation, and two isochoric steps, where the system may not reach thermal equilibrium even at the respective ends of the two stages due to finite-time interaction intervals. Using two-time projective measurement method, we find the probability distribution functions of both coefficient of performance and cooling load, which are dependent on the time duration along each process. With these distributions we find the analytical expressions for the performance parameters as well as their fluctuations. We then numerically determine the performance and fluctuations for the refrigerator operating with a two-level system employed in a recent experimental implementation. Our results clarify the role of finite-time durations of four processes on the performance and fluctuations of the quantum Otto refrigerators.
Highlights
A refrigerator as an inverse operation of a heat engine transfers energy from a cold thermal bath of temperature Th to a a hot one with temperature Tc by consuming work
We study the thermodynamics of a quantum Otto refrigerator where all the four strokes proceed in finite time, within a framework of stochastic thermodynamics
We have developed a general scheme allowing to determine statistics of cooling rate and coefficient of performance (COP) for a quantum Otto refrigerator by analyzing the time evolution of the two isochores and two adiabats. These performance parameters as well as their statistics are determined by the finite time durations required for completing the two nonadiabatic driving strokes and two isochoric branches with incomplete thermalization
Summary
A refrigerator as an inverse operation of a heat engine transfers energy from a cold thermal bath of temperature Th to a a hot one with temperature Tc by consuming work. The quantum Otto cycle of operation, as a typical example of cyclic machines, is controlled by the segments of time that the working system is coupled to a hot and a cold bath, and by the time interval required to driving the control parameter of the system. It was most studied [1,2,3,4,5, 7, 14, 15] as it is easier to analyze and realize. The average COP ε can be always larger than the conventional thermodynamic COP εth for adiabatic driving, but it can be equal to or smaller than COP εth for nonadiabatic driving
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