Abstract
Once in its non-equilibrium steady state, a nanoscale system coupled to several heat baths may be thought of as a “quantum heat pump”. Depending on the direction of its stationary heat flows, it may function as, e.g., a refrigerator or a heat transformer. These continuous heat devices can be arbitrarily complex multipartite systems, and yet, their working principle is always the same: they are made up of several elementary three-level stages operating in parallel. As a result, it is possible to devise external “black-box” testing strategies to learn about their functionality and performance regardless of any internal details. In particular, one such heat pump can be tested by coupling a two-level spin to one of its “contact transitions”. The steady state of this external probe contains information about the presence of heat leaks and internal dissipation in the device and, also, about the direction of its steady-state heat currents. Provided that the irreversibility of the heat pump is low, one can further estimate its coefficient of performance. These techniques may find applications in the emerging field of quantum thermal engineering, as they facilitate the diagnosis and design optimization of complex thermodynamic cycles.
Highlights
By “quantum heat pump”, we generically mean any stationary multi-level system simultaneously coupled to several energy sources and capable of realizing some energy-conversion cycle, like a heat transformer or a refrigerator [1,2]
This paper is structured as follows: In Section 2, we provide a general introduction to endoreversibility, internal dissipation and heat leaks in continuous quantum thermodynamic cycles
We have shown how black-box testing of a multi-level quantum heat device can provide relevant information, such as the direction of its steady-state heat currents, its degree of irreversibility and even a good estimate of its coefficient of performance
Summary
By “quantum heat pump”, we generically mean any stationary multi-level system simultaneously coupled to several energy sources and capable of realizing some energy-conversion cycle, like a heat transformer or a refrigerator [1,2]. We will consider the following setting: being supplied with an unknown absorption heat pump [43], our aim is to learn as much as possible about its operation by interrogating an external probe In our case, this will be a single two-level spin coupled to any of the “contact transitions” or “frequency filters” of the device [11]. Whenever the heat pump is well approximated by an endoreversible model [2], one can give an estimate of its coefficient of performance based on the frequencies of the open decay channels This black-box testing technique may find application in the design optimization and diagnosis of engineered quantum thermodynamic cycles, and in the study of the complex molecules involved in many energy-conversion biological processes.
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