弱驱动过程有效范围的自洽准则
A self-consistent criterion for the range of validity of weakly driven processes
AI总结：
本文提出了一种自洽准则，用于判断弱驱动过程中线性响应的有效范围，通过典型长度尺度和实例验证，提供了热力学与信息论的解释。
摘要：
线性响应理论中一个长期存在的开放性问题在于其真正的有效性范围。确定何时可以信任线性近似通常需要了解二阶修正，而这些修正往往难以显式计算。在本文中，我提出了一种自洽准则，用于线性响应有效性的判断，该准则以理论本身中出现的典型长度尺度形式提出。该结果适用于经典开放系统。我通过布朗粒子在谐振陷阱中的显式例子以及展现Kibble-Zurek机制的经典开放系统来说明该准则。最后，我讨论了该典型长度的物理意义，提供了热力学和信息论的解释。
英文摘要：
One of the longstanding open questions in linear response theory concerns its true range of validity. Determining when the linear approximation can be trusted typically requires knowledge of second-order corrections, which are often difficult to compute explicitly. In this letter, I propose a self-consistent criterion for the validity of linear response, formulated in terms of a typical length scale that emerges from the fluctuation-response inequality within the theory itself. The result applies to classical open systems. I illustrate the criterion with explicit examples of Brownian particles in harmonic traps, and classical open systems presenting Kibble-Zurek mechanism. Finally, I discuss the physical meaning of this typical length, providing both thermodynamic and information-theoretic interpretations.
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