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Journal of Physics D Applied Physics

Ecological optimization of quantum spin-1/2 heat engine at the classical limit

Tzong-Huei Chen

Published Mar 17, 2006• 16 citations
Publisher

Abstract

The purpose of this paper is to present a study of finite-time thermodynamics applied to evaluate the ecological performance of a quantum heat engine which operates between two thermal reservoirs using the working substance of spin-1/2 systems. The quantum heat engine cycle is composed of two isothermal processes, an adiabatic process and an isomagnetic field process. A sequence of time evolution was determined from the quantum angular momentum rate based on the semigroup approach and the quantum master equation. The individual time duration is added to account for the total cycle time. The objective ecological function representing a compromise between power output and irreversibility is maximized with respect to cycle temperature ratio. Effects of thermal reservoir temperature ratio and magnetic field ratio on the ecological function have been discussed. A comparison of quantum heat engine performance under maximum ecological function and maximum power conditions is also presented.

DOI
10.1088/0022-3727/39/7/016

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The purpose of this paper is to present a study of finite-time thermodynamics applied to evaluate the ecological performance of a quantum heat engine which operates between two thermal reservoirs using the working substance of spin-1/2 systems. The quantum heat engine cycle is composed of two isothermal processes, an adiabatic process and an isomagnetic field process. A sequence of time evolution was determined from the quantum angular momentum rate based on the semigroup approach and the quantum master equation. The individual time duration is added to account for the total cycle time. The objective ecological function representing a compromise between power output and irreversibility is maximized with respect to cycle temperature ratio. Effects of thermal reservoir temperature ratio and magnetic field ratio on the ecological function have been discussed. A comparison of quantum heat engine performance under maximum ecological function and maximum power conditions is also presented.
It is considered that the cycle of a quantum heat engine using many non-interacting spin-1/2 systems as the working substance is composed of two adiabatic and two isomagnetic field processes and is referred to as a spin quantum Brayton engine cycle. Based on the quantum master equation and semi-group approach, expressions for the efficiency and power output of the cycle are derived. By using numerical solutions, the power output of the heat engine subject to finite cycle duration is optimized. The maximum power output and the corresponding parameters are calculated numerically. The optimal region of the efficiency and the optimal ranges of temperatures of the working substance and times spent on the two isomagnetic field processes are determined, so that the general optimum performance characteristics of the cycle are revealed. Moreover, the optimal performance of the cycle in the high-temperature limit is also analysed in detail. The results obtained here are further generalized, so that they may be directly used to describe the performance of a quantum Brayton heat engine using spin-J systems as the working substance.
A model of a quantum heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting spin-1/2 systems is established in this paper. The quantum heat engine cycle is composed of two isothermal processes and two irreversible adiabatic processes and is referred to as a spin quantum Carnot heat engine. Based on the quantum master equation and the semi-group approach, equations of some important performance parameters, such as power output, efficiency, entropy generation rate and ecological function (a criterion representing the optimal compromise between exergy output rate and exergy loss rate), for the irreversible spin quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. The effects of internal irreversibility and heat leakage on ecological performance are discussed in detail.
An irreversible cycle model of a quantum heat engine with internal friction is established, which is composed of two adiabatic and two isomagnetic field processes. The working substance of the cycle consists of an ensemble of many non-interacting spin-1/2 systems. Based on a quantum master equation and semi-group approach, the general performance characteristics of the heat engine are investigated. The general expressions for several important parameters, such as the efficiency, power output, and rate of the entropy production, are derived. The performance of the cycle is optimized with respect to the temperatures of the working substance. By numerical solutions, the maximum power output and the corresponding parameters are calculated. The optimal regions of efficiency, temperatures of the working substance, and cycle period are determined. Moreover, the performance of the heat engine in the frictionless case is obtained, which is different from that in the friction case. Finally, the results obtained are generalized to the performance optimization of the heat engine working with spin-J systems.
The cycle model of a regenerative quantum heat engine working with many noninteracting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The inherent regenerative losses in the two constant-frequency processes are calculated. The expressions of several important performance parameters such as the efficiency, power output, and rate of the entropy production are derived for several interesting cases. Especially, the optimal performance of the cycle in high-temperature limit is discussed in detail. The maximum power output and the corresponding parameters are calculated. The optimal region of the efficiency and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined.
It is considered that the cycle of a quantum heat engine working with many non-interacting spin-½ systems is composed of two isothermal and two isomagnetic field processes. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of the efficiency and power output are given. The regenerative losses in two isomagnetic field processes are calculated. The influence of non-perfect regeneration is analysed. Some interesting cases are discussed in detail. The results obtained are further generalized, so that they may be directly used to describe the performance of the quantum heat engine using spin- J systems as the working substance.
In this paper, we consider a model of two-level quantum heat engine to investigate the explicit analytic expression for the thermodynamics quantities in different condition under the finite-time operation. In this engine, the working substance is composed of a spin-half particles immersed in a magnetic field. The finite-time thermodynamic processes consisting of two quantum adiabatic and two quantum isothermal processes. This processes working between two heat reservoirs with an inverse temperatures β1β_{1}β1​ and β2β_{2}β2​ (<β1<β_{1}<β1​). In this processes, we obtain the work, heat, power and efficiency at maximum power output of the model. Our result of the efficiency at maximum power agree with the universal value in the first order of Carnot efficiency.