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Frontiers in Physics

Entangled quantum Stirling heat engine based on two particles Heisenberg model with Dzyaloshinskii-Moriya interaction

H. R. Rastegar Sedehi, Clebson Cruz

Published Jan 22, 2025• 15 citations
Publisher

Abstract

Quantum heat engines have attracted significant attention in recent years due to their potential to surpass classical thermodynamic limits by leveraging quantum effects such as entanglement and coherence. In this study, we analyze a quantum Stirling heat engine characterized by a working substance composed of a two-particle Heisenberg model with Dzyaloshinskii–Moriya (DM) interaction under an external magnetic field. We investigate the impact of the antisymmetric interaction on the engine’s efficiency across varying coupling parameters. Our findings demonstrate that the utilization of a two-qubit Heisenberg model in an entangled quantum Stirling heat engine can significantly enhance efficiency and performance. By optimizing the antisymmetric exchange parameters, we achieve substantial enhancements in engine efficiency, with results demonstrating that the efficiency attains remarkably high values compared to other cycles utilizing the same working substance. These enhancements are primarily influenced by the DM interaction and the entangled states of the working substance, leading to superior performance.

DOI
10.3389/fphy.2025.1512998

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Quantum heat engines have attracted significant attention in recent years due to their potential to surpass classical thermodynamic limits by leveraging quantum effects such as entanglement and coherence. In this study, we analyze a quantum Stirling heat engine characterized by a working substance composed of a two-particle Heisenberg model with Dzyaloshinskii–Moriya (DM) interaction under an external magnetic field. We investigate the impact of the antisymmetric interaction on the engine’s efficiency across varying coupling parameters. Our findings demonstrate that the utilization of a two-qubit Heisenberg model in an entangled quantum Stirling heat engine can significantly enhance efficiency and performance. By optimizing the antisymmetric exchange parameters, we achieve substantial enhancements in engine efficiency, with results demonstrating that the efficiency attains remarkably high values compared to other cycles utilizing the same working substance. These enhancements are primarily influenced by the DM interaction and the entangled states of the working substance, leading to superior performance.
Recently, the influences of the Dzyaloshinski-Moriya (DM) interaction on the performances of the basic thermo-dynamical quantities have attracted a lot of attention. A large number of investigations on the quantum coupling systems with DM interaction have been carried out. However, the specific effects of spin-orbit coupling with the performance on the quantum heat engine have not been taken into account in previous studies. DM interaction is a special kind spin-orbit coupling. To enrich the research of the quantum heat engines, the investigation about the effect of DM interaction on its thermodynamic characteristics should be included. In this study, we construct two entangled quantum engines based on spin-1/2 systems with different DM interactions, with the spin exchange constant and magnetic field fixed. The quantum Otto engine and the quantum Stirling engine are discussed in this article. By numerical calculation, we obtain the expressions for several thermodynamic quantities and plot the isoline maps of the variation of the basic thermodynamic quantities such as heat transfer, work with D1 and D2 and their efficiency in the two engines. The results indicate that the DM interaction plays an important role in the thermodynamic quantities for the quantum Otto engine and the quantum Stirling engine. In addition, the positive work condition is discussed with different DM interactions, with the spin exchange constant and magnetic field. Furthermore fixed, it is found that the efficiency of quantum Otto engine cycle is smaller than the Carnot efficiency while the quantum Stirling cycle can exceed the Carnot efficiency by using the regenerator. Finally, the second law of thermodynamics is shown to be valid in the two entangled quantum systems.
Abstract This study presents the development of an entangled quantum Stirling heat engine based on a two-qubit Heisenberg model. We investigate the impact of entangled states of the working substance on the energy exchange and the performance of the Stirling cycle. The results show an improvement in the cycle’s performance, which is accomplished by changing the entangled states. Furthermore, the results suggest that the operational modes of the quantum cycle can be controlled by considering changes in the entangled states of the working material and the temperatures of the reservoirs.
Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.
A quantum heat engine (QHE) model by considering as working substance two spins (spin-1, spin-[Formula: see text]) is proposed. It consists of using different Heisenberg models with the Dzyaloshinskii-Moriya (DM) interaction in the presence of magnetic field [Formula: see text]. The proposed model contains four stroke two isochoric and two others adiabatic. A comparison of different models such that [Formula: see text], [Formula: see text] and [Formula: see text] is examined for various thermodynamics quantities, especially the efficiency [Formula: see text] and work [Formula: see text]. Finally, discussion and interpretation all results are given in the last section.
In this paper, we consider a heat engines composed of two interactional qubits with spin-orbit interaction (Dzyaloshinskii-Moriya (DM)) subject to an external magnetic field, so that each qubit is coupled with cold or hot source. One intention of this work is to investigate the following question: is it possible the effects of DM lead to improve basic thermodynamic quantities in this heat engine are coupled to local environments that are not necessarily at equilibrium? Moreover, we study whether or not quantum correlations can be helpful in the performance of quantum work engines. For this end, we investigate the effects of the temperature and the interaction rate of each qubit with its surrounding environment on quantum correlations such as quantum coherence and quantum discord and quantum entanglements, as well as the generated work. Finally we compare three quantum correlations (entanglement, discord, and coherence) with thermodynamic parameters and show that the output work is positive for what values of the magnetic field so that this cycle can be considered as a thermal machine.
ABSTRACT We investigate a quantum Stirling engine whose working medium is a three‐qubit Heisenberg XXZ spin chain incorporating the Dzyaloshinskii‐Moriya interaction. The integration of a regenerator, which recovers internal energy during the isochoric processes, significantly enhances the efficiency of the engine, allowing it to approach the Carnot efficiency under appropriate parameters. Our analysis reveals a pronounced stage dependence of quantum correlations: at the end of the isothermal expansion, quantum entanglement and coherence of the thermal equilibrium state are positively correlated with the cycle efficiency, whereas at the end of the isothermal compression, they are negatively correlated with the efficiency. Furthermore, we demonstrate how external magnetic fields and coupling coefficients regulate these quantum correlations and the engine performance, including the work output and efficiency. This work provides a systematic comparison of the stage‐dependent roles of entanglement and coherence in a three‐qubit Stirling cycle, offering insights for designing high‐performance regenerative quantum thermal devices.