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arXiv 0803.0719cond-mat.stat-mechnlin.CD
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涨落耗散:统计物理学中的响应理论

Fluctuation-Dissipation: Response Theory in Statistical Physics

Umberto Marini Bettolo Marconi, Andrea Puglisi, Lamberto Rondoni, Angelo Vulpiani

摘要:

一般方面的波动耗散关系(FDR)和响应理论被认为是。在分析了统计力学中涨落的概念和历史相关性之后,我们说明了自发涨落的弛豫与对外部扰动的响应之间的关系。这些研究可以追溯到爱因斯坦对布朗运动的研究,由奈奎斯特和昂萨格继续进行,最终形成了久保的线性响应理论。FDR最初是在哈密顿系统的统计力学的框架下发展起来的,然而,广义FDR在相当一般的假设下成立,而不管系统的哈密顿量或平衡性质如何。在过去的十年中,这个主题是复活的作品涨落关系(FR)涉及远离平衡系统。分析了这些工作与大偏差理论的联系。除了统计力学的标准应用外,还讨论了波动发挥重要作用的一些例子:流体、颗粒介质、纳米系统和生物系统。

英文摘要:

General aspects of the Fluctuation-Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we illustrate the relation between the relaxation of spontaneous fluctuations, and the response to an external perturbation. These studies date back to Einstein's work on Brownian Motion, were continued by Nyquist and Onsager and culminated in Kubo's linear response theory. The FDR has been originally developed in the framework of statistical mechanics of Hamiltonian systems, nevertheless a generalized FDR holds under rather general hypotheses, regardless of the Hamiltonian, or equilibrium nature of the system. In the last decade, this subject was revived by the works on Fluctuation Relations (FR) concerning far from equilibrium systems. The connection of these works with large deviation theory is analyzed. Some examples, beyond the standard applications of statistical mechanics, where fluctuations play a major role are discussed: fluids, granular media, nano-systems and biological systems.

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