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Physical Review

Quantum Equivalent of the Carnot Cycle

J. E. Geusic, E. O. Schulz-DuBios, H. E. D. Scovil

Published Apr 10, 1967• 236 citations
Publisher

Abstract

The concept of a quantum heat pump is proposed as a convenient model in the thermodynamic interpretation of certain multilevel processes. The ideal quantum heat engine is defined as an idealization of realistic pumped multilevel systems in much the same way that the well-known Carnot cycle is an idealization of physically realizable, classical processes or engines. There is evidence that the conventional Carnot cycle can be operated only between reservoirs at absolute temperatures of identical sign. No such restriction applies, however, to the quantum heat engine. Thus it may be used to calibrate negative absolute temperatures by relating them directly to positive temperatures. Negative efficiencies or efficiencies greater than unity have particularly simple interpretations in the quantum-heat-engine model. An important application of these concepts is in the calculation of optical maser parameters.

DOI
10.1103/physrev.156.343

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The concept of a quantum heat pump is proposed as a convenient model in the thermodynamic interpretation of certain multilevel processes. The ideal quantum heat engine is defined as an idealization of realistic pumped multilevel systems in much the same way that the well-known Carnot cycle is an idealization of physically realizable, classical processes or engines. There is evidence that the conventional Carnot cycle can be operated only between reservoirs at absolute temperatures of identical sign. No such restriction applies, however, to the quantum heat engine. Thus it may be used to calibrate negative absolute temperatures by relating them directly to positive temperatures. Negative efficiencies or efficiencies greater than unity have particularly simple interpretations in the quantum-heat-engine model. An important application of these concepts is in the calculation of optical maser parameters.
Quantum heat engines employ as working agents multilevel systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines, employing two-level atoms as working agents, are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps and negative temperatures are considered.
Conventional heat engines convert thermal energy into mechanical work by using a working medium such as steam or gas that operates between a hot and a cold reservoir. The medium absorbs heat from the hot reservoir, produces work, then releases some heat to the cold reservoir and returns to the initial state. With the advancement of quantum technologies, researchers strive to understand whether quantum media, such as atoms, spins, superconducting circuits and semiconductor quantum dots, can be used in quantum counterparts of the classical heat engines. After a recap of the basics of classical heat engines, this review explores the theoretical foundations and advancements of quantum heat engines, focusing on the proposed two- and multilevel systems used as the working medium for the quantum Otto cycle, which is the ideal thermodynamic cycle that describes the operation of a spark-ignition internal combustion engine. The review compares the efficiency and the work extraction of these systems, discussing their performance in the high- and low-temperature limits. Alternative cycles and engines are also presented to establish the adaptability of the working media when operating under different processes and non-equilibrium conditions. In conclusion, the review offers possible applications and future developments of quantum heat engines.
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.
The quantum analog of Carnot cycles in few-particle systems consists of two quantum adiabatic steps and two isothermal steps. This construction is formally justified by use of a minimum work principle. It is then shown, using minimal assumptions of work or heat in nanoscale systems, that the heat-to-work efficiency of such quantum heat engine cycles can be further optimized via two conditions regarding the expectation value of some generalized force operators evaluated at equilibrium states. In general the optimized efficiency is system specific, lower than the Carnot efficiency, and dependent upon both temperatures of the cold and hot reservoirs. Simple computational examples are used to illustrate our theory. The results should be an important guide towards the design of favorable working conditions of a realistic quantum heat engine.
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
A cyclic thermodynamic heat engine,which combines adiabatic and isothermal processes and consists of classical ideal gas as working substance,runs most efficiently if it is reversible.In this paper,A new cyclic model of quantum Carnot heat engine whose working substance consists of non-interacting extreme relativistic particles confined to an infinite potential well,is set up.It is shown that the engine whose cycle consists of adiabatic and isothermal quantum processes are close analogues of the corresponding classical processes and that the efficiency of this engine is equal to the Carnot efficiency because quantum dynamics is reversible.Consequently,the expectation value of the Hamiltonian in the expression of the efficiency is similar to the temperature in that of the classical one.