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arXiv:1705.08625 · Physical review. E

Quantum thermodynamic cycle with quantum phase transition

Yuhan Ma, Shanhe Su, Chang-Pu Sun

Published Aug 21, 2017• 84 citations
arXivHTMLPDF

Abstract

With the Lipkin-Meshkov-Glick (LMG) model as an illustration, we construct a thermodynamic cycle composed of two isothermal processes and two isomagnetic field processes, and we study the thermodynamic performance of this cycle accompanied by the quantum phase transition (QPT). We find that for a finite particle system working below the critical temperature, the efficiency of the cycle is capable of approaching the Carnot limit when the external magnetic field λ_{1} corresponding to one of the isomagnetic processes reaches the cross point of the ground states' energy level, which can become the critical point of the QPT in the large-N limit. Our analysis proves that the system's energy level crossings at low-temperature limits can lead to a significant improvement in the efficiency of the quantum heat engine. In the case of the thermodynamics limit (N→∞), the analytical partition function is obtained to study the efficiency of the cycle at high- and low-temperature limits. At low temperatures, when the magnetic fields of the isothermal processes are located on both sides of the critical point of the QPT, the cycle reaches maximum efficiency, and the Carnot efficiency can be achieved. This observation demonstrates that the QPT of the LMG model below critical temperature is beneficial to the thermodynamic cycle's operation.

DOI
10.1103/physreve.96.022143

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With the Lipkin-Meshkov-Glick (LMG) model as an illustration, we construct a thermodynamic cycle composed of two isothermal processes and two isomagnetic field processes, and we study the thermodynamic performance of this cycle accompanied by the quantum phase transition (QPT). We find that for a finite particle system working below the critical temperature, the efficiency of the cycle is capable of approaching the Carnot limit when the external magnetic field λ_{1} corresponding to one of the isomagnetic processes reaches the cross point of the ground states' energy level, which can become the critical point of the QPT in the large-N limit. Our analysis proves that the system's energy level crossings at low-temperature limits can lead to a significant improvement in the efficiency of the quantum heat engine. In the case of the thermodynamics limit (N→∞), the analytical partition function is obtained to study the efficiency of the cycle at high- and low-temperature limits. At low temperatures, when the magnetic fields of the isothermal processes are located on both sides of the critical point of the QPT, the cycle reaches maximum efficiency, and the Carnot efficiency can be achieved. This observation demonstrates that the QPT of the LMG model below critical temperature is beneficial to the thermodynamic cycle's operation.
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.
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.
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.
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.
The finite-time operation of a quantum-mechanical heat engine with a working fluid consisting of many noninteracting spin-1/2 systems is considered. The engine is driven by an external, time-dependent and nonrotating magnetic field. The cycle of operation consists of two adiabats and two isotherms. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are developed. The irreversible operation of this engine is studied in three cases: (1) The sudden limit, where the performance is found to be the same as that of the spin analog of the Otto cycle. This case provides the lower bound of efficiency. (2) The step-cycle operation scheme. Here, the optimization of power is carried out in the high-temperature limit (the ‘‘classical’’ limit). The results obtained are similar to those of Andresen et al. [Phys. Rev. A 15, 2086 (1977)]. (3) The Curzon–Ahlborn operation scheme. The semigroup approach is used to model the dynamics. Then the power production is optimized. All the results obtained for Newtonian engines operating by the same scheme, such as the Curzon–Ahlborn efficiency, apply in the high-temperature limit. These results are obtained without the additional assumption of proximity to thermal equilibrium, implicitly implied by the use of Newtonian heat conduction in the original derivation. It seems that the results of the Curzon–Ahlborn analysis are always obtained in the high-temperature limit, irrespective of the details of the model. The performance beyond the classical limit is optimized numerically. The classical approximation is found to be valid for most of the spin-polarization range. The deviations from the classical limit depend heavily upon the specific nature of both the working fluid and the heat baths and exhibit great diversity and complexity.
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.