AI 中文总结
研究有限时间量子奥托发动机，用Lipkin-Meshkov-Glick模型作工作介质，在规范不变量子热力学框架内推导热力学量表达式，分析循环与驱动速度、系统大小关系，揭示临界性影响，建立规范不变热力学等之间的联系。
AI 中文摘要
我们在规范不变量子热力学框架内研究有限时间量子奥托发动机，使用Lipkin-Meshkov-Glick模型作为工作介质。在此公式中，热力学量在热力学不可区分状态的等价类上定义，自然导致功、热、熵和效率的规范不变概念。我们推导了这些量的显式表达式，表明幺正冲程期间的常规功分解为与瞬时能谱和布居变化相关的不变贡献，以及由有限时间量子相干产生的相干贡献。这种分解导致发动机效率和熵产生的相应分裂，为有限时间不可逆性提供了几何解释，并阐明了相干在功提取中的作用。通过分析循环对驱动速度和系统大小的依赖性，我们确定了发动机的运行区域并研究了临界性的影响。我们表明，穿过临界区域会大大减小循环作为热机运行的参数空间。同时，只要发动机条件得到满足，传统描述和规范不变描述之间的差异就会受到强烈抑制，表明规范不变部分主要承载提取的功。这些结果在规范不变热力学、有限时间不可逆性和多体量子热机中的功提取之间建立了直接联系。
英文摘要
We investigate a finite-time quantum Otto engine within the framework of gauge-invariant quantum thermodynamics, using the Lipkin-Meshkov-Glick model as the working medium. In this formulation, thermodynamic quantities are defined on equivalence classes of thermodynamically indistinguishable states, leading naturally to gauge-invariant notions of work, heat, entropy, and efficiency. We derive explicit expressions for these quantities and show that the usual work performed during the unitary strokes decomposes into an invariant contribution, associated with changes in the instantaneous energy spectrum and populations, and a coherent contribution arising from finite-time quantum coherences. This decomposition induces the corresponding splittings of engine efficiency and entropy production, providing a geometric interpretation of finite-time irreversibility and clarifying the role of coherence in work extraction. By analyzing the cycle's dependence on driving speed and system size, we identify the engine's operating region and investigate the influence of criticality. We show that crossing the critical region substantially reduces the parameter space in which the cycle operates as a heat engine. At the same time, whenever the engine condition remains satisfied, the discrepancy between the conventional and gauge-invariant descriptions becomes strongly suppressed, indicating that the gauge-invariant sector predominantly carries the extracted work. These results establish a direct connection between gauge-invariant thermodynamics, finite-time irreversibility, and work extraction in many-body quantum thermal machines.
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