Abstract
In this work we considered the quantum Otto cycle within an optimization framework. The goal was maximizing the power for a heat engine or maximizing the cooling power for a refrigerator. In the field of finite-time quantum thermodynamics it is common to consider frictionless trajectories since these have been shown to maximize the work extraction during the adiabatic processes. Furthermore, for frictionless cycles, the energy of the system decouples from the other degrees of freedom, thereby simplifying the mathematical treatment. Instead, we considered general limit cycles and we used analytical techniques to compute the derivative of the work production over the whole cycle with respect to the time allocated for each of the adiabatic processes. By doing so, we were able to directly show that the frictionless cycle maximizes the work production, implying that the optimal power production must necessarily allow for some friction generation so that the duration of the cycle is reduced.
Highlights
Quantum models of heat engines and refrigerators have been investigated extensively, especially because of the relevance of these models to the problem of cooling at extremely low temperatures, i.e., near absolute zero
We consider the typical optimization perspective assumed in the field of finite-time thermodynamics: maximization of the average power extracted from a heat-engine [7,8,9] or the average cooling power provided by a refrigerator [3,10]
As mentioned in the introduction, we will show that the trajectories leading to maximum average power are not frictionless cycles
Summary
Quantum models of heat engines and refrigerators have been investigated extensively, especially because of the relevance of these models to the problem of cooling at extremely low temperatures, i.e., near absolute zero. Abah et al [15,16], frictionless trajectories have been shown to be the optimal finite-time processes that connect two different thermal states while guaranteeing maximal work extraction, i.e., equal to that obtained in the quasi-static limit These analyses are often very insightful [1,17,18], due to the fact that the resulting cycles are mathematically simpler to investigate, thereby admitting analytical computation of, e.g., power and efficiency. We consider quantum heat engines and refrigerators with different working fluids, namely, an ensemble of spin systems All these other cases are shown to be analogous to the harmonic heat engine in that frictionless cycles are not providing maximal power with respect to the time allocation
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