Statistical Mechanics: J Theory and Experiment Beyond the linear fluctuation-dissipation theorem: the role of causality
Statistical Mechanics: J Theory and Experiment Beyond the linear fluctuation-dissipation theorem: the role of causality
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统计力学：J 理论与实验 超越线性注量耗散定理：因果关系的作用
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通讯作者：
G. Branstator
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作者：
F. Selten;G. Branstator
.在本文中，我们解决了传统的问题有关的波动的系统，其响应外部强迫和扩展的经典理论，以便能够包括非线性过程。有了这个目标，我们试图建立在久保的线性响应理论和响应理论最近开发的Ruelle的非平衡系统配备了一个不变的Sinai-Ruelle-Bowen（SRB）措施。我们的推导也揭示了因果关系之间的联系和相关的波动和响应的可能性，无论是在线性和非线性水平。我们首先显示，在一个相当一般的设置，如何Ruelle的反应理论的形式主义可以用来在一个新的方式来推导一个推广的Kramers-Kronig关系。然后，我们提供了一个正式的扩展，在每一个顺序的非线性的波动耗散定理的一般系统赋予一个光滑不变的措施。最后，我们专注于从平衡弱扰动系统的物理相关的情况下，我们提出了明确的涨落耗散关系连接的磁化率描述的n阶响应的系统与适当定义的相关性在平衡系综。
. In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With this goal, we try to build on Kubo’s linear response theory and the response theory recently developed by Ruelle for nonequilibrium systems equipped with an invariant Sinai–Ruelle–Bowen (SRB) measure. Our derivation also sheds light on the link between causality and the possibility of relating fluctuations and response, both at the linear and nonlinear level. We first show, in a rather general setting, how the formalism of Ruelle’s response theory can be used to derive in a novel way a generalization of the Kramers–Kronig relations. We then provide a formal extension at each order of nonlinearity of the fluctuation-dissipation theorem for general systems endowed with a smooth invariant measure. Finally, we focus on the physically relevant case of systems weakly perturbed from equilibrium, for which we present explicit fluctuation-dissipation relations linking the susceptibility describing the n th order response of the system with suitably defined correlations taken in the equilibrium ensemble.