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arXiv 2501.01050cond-mat.stat-mechphysics.bio-ph
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统一的线性波动-响应理论:任意远离平衡

Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium

University of North Carolina-Chapel Hill(北卡罗来纳大学教堂山分校)

Jiming Zheng, Zhiyue Lu

AI总结:

本文提出了一种统一的线性波动-响应理论,适用于任意远离平衡的马尔可夫过程,通过分解局部动态事件的空间相关性,揭示了响应特性编码在转换和停留时间之间的相关性,并扩展了非平衡线性响应关系。

摘要:

理解系统对外部扰动的响应是物理学中的基本挑战,特别是对于非平衡和非稳态过程。波动-耗散定理为近平衡系统提供了一个完整的框架,近年来已有关于特定非平衡领域的各种界限报告。本文提出了一种精确的响应等式,适用于任意马尔可夫过程,将系统响应分解为局部动态事件的空间相关性。这种分解揭示了响应特性编码在网络中转换和停留时间之间的相关性中,为波动-耗散定理和最近发展的非平衡线性响应关系提供了自然推广。我们的理论统一了现有的响应界限,将其扩展到时间依赖过程,并揭示了多参数响应不等式紧致性的基本单调性性质。除了理论意义外,该框架使从采样未受扰动轨迹中高效评估响应特性成为可能,为估计复杂网络和生物系统远离平衡时的响应特性提供了传统有限差分方法无法比拟的优势。

英文摘要:

Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for near-equilibrium systems, and various bounds have recently been reported for specific non-equilibrium regimes. Here, we present an exact response equality for arbitrary Markov processes that decompose system response into spatial correlations of local dynamical events. This decomposition reveals that response properties are encoded in correlations between transitions and dwelling times across the network, providing a natural generalization of the fluctuation-dissipation theorem and recently developed non-equilibrium linear response relations. Our theory unifies existing response bounds, extends them to time-dependent processes, and reveals fundamental monotonicity properties of the tightness of multi-parameter response inequalities. Beyond its theoretical significance, this framework enables efficient numerical evaluation of response properties from sampling unperturbed trajectories, offering significant advantages over traditional finite-difference approaches for estimating response properties of complex networks and biological systems far from equilibrium.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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