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arXiv:0811.2756 · Physical Review E

Quantum thermodynamic cycles and quantum heat engines. II.

H. T. Quan

Published Apr 20, 2009• 209 citations
arXivHTMLPDF

Abstract

We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.

DOI
10.1103/physreve.79.041129

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We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.
We evaluate quantum Otto, Diesel and Brayton cycles employing multiple-state 1D box system instead of ideal gas filled cylinder. The work and heat are extracted using the change in the expectation of Hamiltonian of the system which leads to the first law of thermodynamics to quantum system. The first law makes available to redefine the force which is in fact not well defined in a quantum mechanical system and then it is applied to define the quantum version of thermodynamic processes, i.e. isobaric, isovolume and adiabatic. As the results, the efficiency of quantum Otto engine depends only on the compression ratio and will be higher than the efficiency of quantum Diesel which can decrease by the widening of expansion under isobaric process. The efficiency of quantum Brayton engine may reach maximum on certain combination between the wide of box under isobaric expansion and compression, under certain conditions. The amount of levels participated in the quantum heat engine system will potentially reduce the performance of the quantum heat cycles consisting isobaric process, but it can be resisted using isobaric process controller.
We explore the quantum version of Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process, one corresponds to the external magnetic field (characterized by FxF_xFx​) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by FyF_yFy​). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by FxF_xFx​), whereas the subsystem's cycle is of quantum Otto in another Brayton cycle (characterized by FyF_yFy​). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system are usually larger than the sum of work done by the two subsystems. The other interesting finding is that for the cycle characterized by FyF_yFy​, the subsystem can be a refrigerator while the total system is a heat engine. The result in the paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.
We explore the quantum version of the Brayton cycle with a composite system as the working substance. The actual Brayton cycle consists of two adiabatic and two isobaric processes. Two pressures can be defined in our isobaric process; one corresponds to the external magnetic field (characterized by F(x)) exerted on the system, while the other corresponds to the coupling constant between the subsystems (characterized by F(y)). As a consequence, we can define two types of quantum Brayton cycle for the composite system. We find that the subsystem experiences a quantum Brayton cycle in one quantum Brayton cycle (characterized by F(x)), whereas the subsystem's cycle is quantum Otto cycle in another Brayton cycle (characterized by F(y)). The efficiency for the composite system equals to that for the subsystem in both cases, but the work done by the total system is usually larger than the sum of the work done by the two subsystems. The other interesting finding is that for the cycle characterized by F(y), the subsystem can be a refrigerator, while the total system is a heat engine. The result in this paper can be generalized to a quantum Brayton cycle with a general coupled system as the working substance.
Quantum heat engines are devices comprised of one or more quantum systems operating cyclically between two heat reservoirs to produce work.Although the laws of quantum mechanics rule these engines, this does not imply that these machines function in a quantum fashion, or exhibit a quantum advantage.Indeed, quantum heat engines have shown a remarkable similarity with classical models, thus raising the question of what is "quantum" in quantum thermodynamics.With the help of the P-representability concept, an expression called classicality function is introduced -allowing us to quantify the degree of non-classicality of a bosonic system.As an illustration, we consider a quantum heat engine consisting of a single bosonic mode as a working substance coupled to a cold thermal and hot squeezed thermal bath.For two specific protocols, i.e., a quantum Otto and a generalized cycle, we show that the non-classicality is a resource that can be used to perform thermodynamical tasks more efficiently.Furthermore, we present a theoretical framework to study how quantum features, such as entanglement or coherence, affect the classical formulations of thermodynamic axioms.
In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwell's demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.