<p>The quantum thermodynamic performance of a Stirling cycle employing a three-spin Lipkin-Meshkov-Glick (LMG) model is investigated under varying magnetic interaction anisotropies and control parameters. The model operates in the anisotropic XY regime (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\gamma =+1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>), the Ising limit (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\gamma =0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>), and the mixed ferromagnetic regime (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\gamma =-1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>), with key thermodynamic quantities evaluated across a range of temperature ratios, magnetic field strengths, and coupling asymmetries. The mean energy landscape reveals a strong dependence on the anisotropy parameter, highlighting quantum coherence effects and spin alignment. The operational phase space is mapped, showing distinct transitions between heat engine, refrigerator, and heater modes, with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\gamma =+1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> exhibiting the broadest mode diversity and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\gamma =-1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> yielding robust engine-like behavior. Thermodynamic quantities such as heat exchange and work output are analyzed, showing mode transitions driven by magnetic field tuning. Efficiency, refrigeration performance (ε), and the refined performance coefficient (Π) are presented, revealing intricate dependencies on system parameters. Anisotropic spin coupling is shown to enhance thermodynamic responsiveness, while strong magnetic fields induce saturation and performance decline due to level polarization. The results demonstrated that quantum many-body interactions, when properly tuned, could be harnessed to optimize the design of nanoscale heat engines, refrigerators, and other quantum thermal devices.</p>

Thermodynamic Performance of a Quantum Stirling Engine with a Three-spin LMG Model under Anisotropic Coupling

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发表日期：

2026年2月24日

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Minghui Ou,
Tong Zhou,
Li-Cai Zhao

摘要

The quantum thermodynamic performance of a Stirling cycle employing a three-spin Lipkin-Meshkov-Glick (LMG) model is investigated under varying magnetic interaction anisotropies and control parameters. The model operates in the anisotropic XY regime ( $\gamma =+1$ $γ = + 1$ ), the Ising limit ( $\gamma =0$ $γ = 0$ ), and the mixed ferromagnetic regime ( $\gamma =-1$ $γ = - 1$ ), with key thermodynamic quantities evaluated across a range of temperature ratios, magnetic field strengths, and coupling asymmetries. The mean energy landscape reveals a strong dependence on the anisotropy parameter, highlighting quantum coherence effects and spin alignment. The operational phase space is mapped, showing distinct transitions between heat engine, refrigerator, and heater modes, with $\gamma =+1$ $γ = + 1$ exhibiting the broadest mode diversity and $\gamma =-1$ $γ = - 1$ yielding robust engine-like behavior. Thermodynamic quantities such as heat exchange and work output are analyzed, showing mode transitions driven by magnetic field tuning. Efficiency, refrigeration performance (ε), and the refined performance coefficient (Π) are presented, revealing intricate dependencies on system parameters. Anisotropic spin coupling is shown to enhance thermodynamic responsiveness, while strong magnetic fields induce saturation and performance decline due to level polarization. The results demonstrated that quantum many-body interactions, when properly tuned, could be harnessed to optimize the design of nanoscale heat engines, refrigerators, and other quantum thermal devices.