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arXiv:2111.12467 · Journal of Applied Physics

Finite-time quantum measurement cooling beyond the Carnot limit

Tong Fu, Youlin Wang, Jingyi Chen, Jianying Du, Jincan Chen, Chikako Uchiyama, Shanhe Su

Published Jul 10, 2023• 2 citations
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Abstract

We proposed the finite-time cycle model of a measurement-based quantum cooler, where the invasive measurement provides the power to drive the cooling cycle. Such a cooler may be regarded as an alternative thought experiment of Maxwell’s demon. The measurement-feedback information is capable of moving heat from the cold to hot bath without any work input and even making the maximum coefficient of performance larger than the Carnot limit. The causes that this seemingly paradoxical result does not violate the laws of thermodynamics can be clearly explained through the derivation of a generalized Clausius inequality including the mutual information.

DOI
10.1063/5.0154341

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We proposed the finite-time cycle model of a measurement-based quantum cooler, where the invasive measurement provides the power to drive the cooling cycle. Such a cooler may be regarded as an alternative thought experiment of Maxwell’s demon. The measurement-feedback information is capable of moving heat from the cold to hot bath without any work input and even making the maximum coefficient of performance larger than the Carnot limit. The causes that this seemingly paradoxical result does not violate the laws of thermodynamics can be clearly explained through the derivation of a generalized Clausius inequality including the mutual information.
We discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time.
We study the physical mechanism of Maxwell's demon (MD), which helps do extra work in thermodynamic cycles with the heat engine. This is exemplified with one molecule confined in an infinitely deep square potential with a movable solid wall. The MD is modeled as a two-level system (TLS) for measuring and controlling the motion of the molecule. The processes in the cycle are described in a quantum fashion. It is discovered that a MD with quantum coherence or one at a temperature lower than the molecule's heat bath can enhance the ability of the whole working substance, formed by the heat engine plus the MD, to do work outside. This observation reveals that the essential role of the MD is to drive the whole working substance off equilibrium, or equivalently, to work between two heat baths with different effective temperatures. The elaborate studies with this model explicitly reveal the effect of finite size off the classical limit or thermodynamic limit, which contradicts common sense on a Szilard heat engine (SHE). The quantum SHE's efficiency is evaluated in detail to prove the validity of the second law of thermodynamics.
We consider a quantum endoreversible Carnot engine cycle and its inverse operation–Carnot refrigeration cycle, working between a hot bath of inverse temperature βh and a cold bath at inverse temperature βc. For the engine model, the hot bath is constructed to be squeezed, whereas for the refrigeration cycle, the cold bath is set to be squeezed. In the high-temperature limit, we analyze efficiency at maximum power and coefficient of performance at maximum figure of merit, revealing the effects of the times allocated to two thermal-contact and two adiabatic processes on the machine performance. We show that, when the total time spent along the two adiabatic processes is negligible, the efficiency at maximum power reaches its upper bound, which can be analytically expressed in terms of squeezing parameter r: ηana∗=1−sech[2r]1−ηC, with the Carnot efficiency ηC=1−βh/βc and the coefficient of performance at maximum figure of merit is bounded from the upper side by the analytical function: εana∗=1+εCsech[2r](1+εC)−εC−1, where εC=βh/(βc−βh).
We investigated coupled-qubit-based thermal machines powered by quantum measurements and feedback. We considered two different versions of the machine: (1) a quantum Maxwell's demon, where the coupled-qubit system is connected to a detachable single shared bath, and (2) a measurement-assisted refrigerator, where the coupled-qubit system is in contact with a hot and cold bath. In the quantum Maxwell's demon case, we discuss both discrete and continuous measurements. We found that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further found that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we used continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We found that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements.
Heat engines constitute the major building blocks of modern technologies. However, conventional heat engines with higher power yield lesser efficiency and vice versa and respect various power-efficiency trade-off relations. This is also assumed to be true for the engines operating in the quantum regime. Here we show that these relations are not fundamental. We introduce quantum heat engines that deliver maximum power with Carnot efficiency in the one-shot finite-size regime. These engines are composed of working systems with a finite number of quantum particles and are restricted to one-shot measurements. The engines operate in a one-step cycle by letting the working system simultaneously interact with hot and cold baths via semilocal thermal operations. By allowing quantum entanglement between its constituents and, thereby, a coherent transfer of heat from hot to cold baths, the engine implements the fastest possible reversible state transformation in each cycle, resulting in maximum power and Carnot efficiency. Finally, we propose a physically realizable engine using quantum optical systems.