The cycle model of a quantum refrigerator composed of two isothermal and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin- 1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. Especially, the case at high temperatures is analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot refrigerator are derived simply.

The influence of quantum degeneracy on the performance of a Stirling refrigeration cycle is investigated, based on the equation of state of an ideal Fermi gas. The inherent regenerative losses and the coefficient of performance (COP) of the cycle are calculated. It is found that, under the condition of strong gas degeneracy, the COP of the cycle in the first approximation is a function only of the temperatures of the heat reservoirs, while under other conditions, the COPs of the cycle depend on the temperatures of the heat reservoirs and other parameters of the cycle. The results obtained here reveal the general performance characteristics of a Stirling refrigeration cycle having a Fermi gas as its working substance.

The thermodynamic properties of the dielectric materials are analyzed in detail, based on the Curie law, Curie-Weiss law andother relations betweenthe electrical polarization and the electric fieldstren gth. It is proven that the specific heat at constant electrical polarization is only a function of temperature, while the specific heat at constant electric field strength is dependent on the electric field strength and temperature. Moreover, the regenerative characteristics of the electrocaloric Stirling andEricsso n refrigeration cycles are discussed. Some important conclusions are obtained.

The performance of a ferroelectric Ericsson refrigeration cycle is investigated on the basis of the statistic relation between the electrical polarization and the electric field strength of the ferroelectric materials. The inherent regenerative losses in the cycle are calculated. The coefficients of performance of the cycle are derived. Moreover, the performance of the Ericsson refrigeration cycle using other dielectric materials as the working substance is discussed. The results obtained here may reveal the general characteristics of the electrocaloric Ericsson refrigeration cycle.

A general irreversible cycle model of a magnetic Ericsson refrigerator is established. The irreversibilities in the cycle model result from the finite-rate heat transfer between the working substance and the external heat reservoirs, the inherent regenerative loss, the additional regenerative loss due to thermal resistances, and the heat leak loss between the external heat reservoirs. The cycle model is used to optimize the performance of the magnetic Ericsson refrigeration cycle. The fundamental optimum relation between the cooling rate and the coefficient of performance of the cycle is derived. The maximum coefficient of performance, maximum cooling rate and other relevant important parameters are calculated. The optimal operating region of the cycle is determined. The results obtained here are very general and will be helpful for the optimal design and operation of the magnetic Ericsson refrigerators. [DOI: 10.1115/1.1616037]

本文基于理想费米气体的状态方程，分析了以理想费米气体为工质的量子Ericsson制冷循环中的回热特征，推导出其制冷循环的制冷系数表达式，并在高温和低温条件下对制冷系数进行了讨论，这将对低温制冷机的研究提供理论依据。

本文基于量子主方程和半群方法，分析了以谐振子系统为工质的量子制冷循环中的回热特征及时间演化公式，推导出制冷系数、制冷率和输入功率的一般表达式，在高温极限下详细推导出它们的具体优化特征。这里所获得的结论可以与经典制冷循环的结论进行比较，发现有许多类似之处。

基于理想量子气体的状态方程。分析了量子气体斯特林制冷循环中的回热特征,推导出循环的制冷系数一般表达式. 获得了在强简并和弱简并条件下循环的制冷系数，对全面理解气体斯特林制冷机的性能有所帮助。

The irreversible model of a quantum refrigeration cycle composed of two adiabatic and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. It is found that the coefficient of performance of this cycle is close analogues of that ofclassical Carnot cycle. Some performance characteristics curves between the cooling rate and the maximum "temperature" ratio of the workingsubstances are plotted. Further, at high temperatures the optimal relations of the cooling rate and the maximum cooling rate are analyzed indetail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of hequantumrefrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot and Ericsson refrigeration cycles are derived analogously.