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AIP conference proceedings

Efficiency of simple quantum engines: The Joule-Brayton and Otto cycles

Lev Guzmán-Vargas

Published Jan 1, 2002• 4 citations
Publisher

Abstract

Following the formalism of a quantum engine proposed by Bender et al. for a single particle of mass m confined to an infinite one‐dimensional potential well of width L. we construct the isobaric and isochoric quantum analogous processes in order to analyze the efficiency of two classical thermodynamic engines: The Joule‐Brayton and Otto cycles. We find that the efficiency are analogous to those obtained for classical engines.

DOI
10.1063/1.1523819

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Following the formalism of a quantum engine proposed by Bender et al. for a single particle of mass m confined to an infinite one‐dimensional potential well of width L. we construct the isobaric and isochoric quantum analogous processes in order to analyze the efficiency of two classical thermodynamic engines: The Joule‐Brayton and Otto cycles. We find that the efficiency are analogous to those obtained for classical engines.
The quantum engine cycle serves as an analogous representation of the macroscopic nature of heat engines and the quantum regime of thermal devices composed of a single element. In this work, we follow the formalism of a quantum engine proposed by Bender et al. [1] where they observed quantum Carnot cycle with a single particle of mass m confined to an infinite one-dimensional potential well of width L as a working medium. Using this model, a quantum-mechanical analogue of the Stirling cycle [SC] and Ericsson cycle [EC] have been constructed through changes of both, the width of the well and its quantum state. The efficiency of quantum engines is derived, which is found to be analogous to classical thermodynamic engines. Keywords: Quantum thermodynamics, Quantum mechanics, Ericsson cycle, Stirling cycle, Quantum heat engines, Nano-engines.
A quantum dual-engine is a machine that applies a dual cycle in a quantum system. This machine is a quantum analogy to the classical dual-engine consisting of a combination of classical Otto engine and classical Diesel engine. By analogizing a particle in a one-dimensional infinite potential well as a gas in a piston-cylinder, quantum thermodynamic processes in a dual cycle can be explained from the analogies of classical processes such as adiabatic, isochoric, and isobar. This research examines the value of thermal efficiency and other aspects of the quantum dual-engine with the study of literature. The results of the research show that the thermal efficiency of the quantum dual-engine has similarities with the classical dual-engine. Under the same mechanical ratios condition, the thermal efficiency of a quantum dual-engine has a higher value than the thermal efficiency of its classical engines.
Quantum Brayton engine efficiency with the massless boson particle as a working substance has been investigated. The research method used is analogy modeling of the first law of classical thermodynamics which is implemented into the quantum systems. The quantum system used is the single massless boson particle trapped inside the two-dimensional symmetrical potential well as a replacement for the classic system is an ideal gas in a piston tube. By replacing the working substance from the classical system into a quantum system, the four processes that form the classic Brayton cycle (two isobaric processes and two adiabatic processes) can be constructed on the quantum system. The final result indicates that the quantum Brayton engine with boson particle has a higher efficiency value compared to the classic version, but is lower than that engine when the massless boson is replaced with nonrelativistic particles. This occurs because of differences in Laplace's constant value in the three systems.
A quantum Brayton engine using a massless Boson trapped in a one-dimensional potential well as a working substance has been constructed to be studied. We used a modified analogical model by the first law of thermodynamics for a quantum system implementation. The system was built with Klein Gordon equation, relativistic quantum mechanics Hamiltonian, without the mass term of the Hamiltonian and it was trapped in a one-dimensional potential well. Then, it underwent the quantum ideal Brayton cycle process. The quantum Brayton process consisted of adiabatic compression, isobaric expansion, adiabatic expansion, and isobaric compression processes. This relativistic quantum mechanics Brayton engine has found that the efficiency formulation was similar to the classical one. This study obtained the conformity results between the quantum relativistic and classical Brayton engines. By this cycle process, we also invented that the ratio of heat capacity under constant pressure and volume of the system was 2. It could indicate that the efficiency of quantum relativistic Brayton engine is higher than the classical one.
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 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.