非平稳系统的形式涨落-响应关系：动态共轭变量
Formal Fluctuation-Response Relations for Non-Stationary Systems: The Dynamic Conjugate Variable
浏览论文内容
中文总结 AI 辅助
本文通过引入动态共轭变量，为马尔可夫非平稳系统推导了涨落-响应关系，该变量为双时间形式，平稳时退化为单时间，并统一了多个已知结果。
中文摘要 AI 辅助
涨落-响应关系（FRRs）将系统对外部扰动的线性响应与未扰动系统中自发涨落的性质联系起来。我们提供了一种针对非平稳动力学的涨落-响应关系的简单推导，该方法遵循几乎标准的方式，基于引入一个与扰动共轭的变量（动态共轭）。该推导仅依赖于底层动力学的马尔可夫性，唯一的额外假设是过程的转移概率密度函数关于恒定、时间无关扰动的强度是可微的。然而，该共轭变量的结构并不寻常：它是一个双时间的变量，在平稳情形下退化为通常的单时间共轭变量。我们展示了若干已知结果如何从这一方法中得出。
英文摘要
Fluctuation-response relations (FRRs) connect the linear response of a system to an external perturbation with properties of spontaneous fluctuations in the unperturbed system. We provide a simple derivation of FRRs for non-stationary dynamics following an almost standard way based on introducing a variable conjugated to perturbation (a dynamic conjugate). The derivation relies solely on the Markovianity of the underlying dynamics, with the only additional assumption that the transition PDF of the process is differentiable with respect to the strength of a constant, time- independent perturbation. The structure of this conjugate variable is however unusual: it is a two-time one, and reduces to a usual single-time conjugate in stationary situations. We show how several known results follow from this approach.
发表机构
- Humboldt-Universität zu Berlin（柏林洪堡大学）
机构由 AI 辅助整理，请以论文原文为准。
