检测多尺度系统中的时间不可逆性：Lorenz96模型中的相关函数与响应函数
Detecting time-irreversibility in multiscale systems: correlation and response functions in the Lorenz96 model
AI总结：
本研究通过高阶相关函数与能量响应函数分析双尺度Lorenz96模型，证明其可检测时间不可逆性，并揭示跨尺度能量输运的不对称性及扰动协议对响应的影响。
摘要：
由于多尺度系统与地球物理系统的相关性，近年来通过统计力学视角研究多尺度系统已受到广泛关注。本研究旨在表征著名的双尺度Lorenz96模型的非平衡性质，该动力学系统常用于测试地球物理学中的思想，我们通过研究高阶相关函数或能量对外部扰动的响应来实现这一目标。这些工具在平衡（无粘性）和非平衡（粘性）系统中均提供了明确证据，表明它们适用于检测时间反演对称性破缺以及表征此类模型中的输运性质。特别地，我们刻画了局域能量扰动在不同尺度间的输运方式，强调天气尺度变量的扰动对平流变量影响显著，而后者对天气尺度的影响几乎可忽略。最后，我们展示了全局可观测量对有限大小扰动的响应强烈依赖于扰动协议，这阻碍了仅通过弛豫过程观测来理解系统物理性质，而这一事实常被忽视。
英文摘要：
Due to their relevance to geophysical systems, the investigation of multiscale systems through the lens of statistical mechanics has gained popularity in recent years. The aim of our work is the characterization of the nonequilibrium properties of the well-known two-scales Lorenz96 model, a dynamical system much used for testing ideas in geophysics, by studying either higher-order correlation functions or response to external perturbations of the energy. These tools in both equilibrium (inviscid) or non-equilibrium (viscous) systems provide clear evidence of their suitability for detecting time-reversal symmetry breaking and for characterizing transport properties also in this class of models. In particular, we characterize how localized energy perturbations are transported between the different scales, highlighting that perturbations of synoptic variables greatly impact advective variables but perturbations of the latter have a practically negligible effect on synoptic scales. Finally, we show that responses of global observables to finite size perturbations strongly depend on the perturbation protocol. This prevents the physical understanding of the system from observations of the relaxation process alone, a fact often overlooked.
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