AI 中文总结
通过引入高斯量子态维格纳 - 费希尔信息的能态分解，建立量子热力学与信息几何联系，推导其解析表达式并分被动和能态贡献，分析能态姆潘巴效应，揭示量子态功与信息几何结构关系。
AI 中文摘要
我们通过引入高斯量子态的维格纳 - 费希尔信息的能态分解，在量子热力学和信息几何之间建立了直接联系。我们根据相空间协方差矩阵和均值向量推导了维格纳 - 费希尔信息的解析表达式，并表明它自然地分为被动和能态贡献。被动项完全由相关被动态的维格纳熵率决定。能态贡献则量化了位移和压缩资源如何改变系统在相空间中的统计速度和轨迹长度。作为应用，我们分析了最近提出的能态姆潘巴效应，并证明它可追溯到与压缩热态相关的被动态的反常几何演化。我们的结果揭示了量子态中可提取的功如何约束其信息几何结构，建立了一个在连续变量量子系统中连接能态、熵产生率和统计几何的框架。
英文摘要
We establish a direct connection between quantum thermodynamics and information geometry by introducing an ergotropic decomposition of the Wigner-Fisher information for Gaussian quantum states. We derive an analytical expression for the Wigner-Fisher information in terms of the phase-space covariance matrix and mean vector, and show that it naturally separates into passive and ergotropic contributions. The passive term is shown to be entirely determined by the Wigner entropy rate of the associated passive state. The ergotropic contribution, in turn, quantifies how displacement and squeezing resources modify the statistical velocity and length of the system trajectory in phase space. As an application, we analyze the recently proposed ergotropic Mpemba effect and demonstrate that it can be traced to the anomalous geometric evolution of the passive state associated with squeezed thermal states. Our results reveal how the extractable work stored in a quantum state constrains its information-geometric structure, establishing a framework that links ergotropy, entropy production rate, and statistical geometry in continuous-variable quantum systems.
Comments12 pages, 3 figures; Comments welcome!
