探索遍历信道中的非马尔可夫性：通过做功能力测量记忆保持
Exploring Non-Markovianity in Ergodic Channels: Measuring Memory Retention through Ergotropy
AI总结：
本文定义并分析具有唯一不动点的量子遍历信道，利用 ergotropy 回流指示非马尔可夫记忆效应，并揭示其在开放量子系统热力学与量子电池中的意义。
摘要：
在本工作中，我们引入并刻画了一类具有唯一不动点的广泛量子操作，称为量子遍历信道。我们在任意有限维度中推导了这些信道的 Lindblad 型主方程，并使用既有测度分析其非马尔可夫动力学。当不动点为被动态时，这些信道表现出具有显著热力学含义的 ergotropy（做功能力）动力学。具体而言，在马尔可夫过程下，ergotropy——衡量系统在幺正演化下可提取功的量——单调下降。然而，在非马尔可夫动力学中，ergotropy 会发生波动，产生回流效应，凸显由记忆诱导的资源恢复。我们的发现表明，这种 ergotropy 回流可作为非马尔可夫性具有操作意义的指标，为开放量子系统中记忆效应与热力学行为之间的相互作用提供新视角。本研究加强了理解遍历信道下能量动力学的理论框架，并强调了探索量子电池中记忆效应含义的新途径。
英文摘要：
In this work we introduce and characterize a broad class of quantum operations with a unique fixed point, termed quantum ergodic channels. We derive Lindblad-type master equations for these channels in arbitrary finite dimensions and analyze their non-Markovian dynamics using established measures. When the fixed point is a passive state, the channels exhibit ergotropy dynamics with notable thermodynamic implications. Specifically, under Markovian processes, ergotropy, a measure of the extractable work from a system under unitary evolution monotonically decreases. However, in non-Markovian dynamics, ergotropy fluctuates, leading to a backflow effect that highlights memory-induced resource recovery. Our findings suggest that this ergotropy backflow could serve as an operationally meaningful indicator of non-Markovianity, offering new perspectives on the interplay between memory effects and thermodynamic behavior in open quantum systems. This study enhances the theoretical framework for understanding energy dynamics under ergodic channels and highlights new avenues for exploring the implications of memory effects in quantum batteries.
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