论文标题
关于宏观波动理论的注释
Notes about the Macroscopic Fluctuating Theory
论文作者
论文摘要
宏观波动理论是从实践和自我一致的角度提出的。我们认为，起点是，假设处于介质刻度的系统是由langevin方程进化的字段$ ϕ（x，t）$描述的，该方程在本地保守或不能保守的。它的动态行为也可能取决于外部代理对散装或/和系统边界的作用。我们得出相应的fokker-planck方程和路径的概率，并使用它们来研究系统固定状态的一般特性。特别是，我们关注的是对定义较小噪声极限的固定分布的准潜电的研究。我们认为，当系统是宏观可逆的时，该系统处于平衡状态，即从固定状态产生波动的最可能的路径等于将其放松的时间逆转路径。当这种情况不发生时，系统处于非平衡固定状态，其准电位可能会出现一些缺乏可怜性和/或远程作用。我们还得出了固定状态下两体相关性的封闭方程，并将其应用于某些典型情况。最后，我们使用大偏差原理获得了广义的绿色kubo公式类别。
The Macroscopic Fluctuating Theory is presented from a practical and self consistent point of view. We take as starting point the assumption that a system at a mesoscopic scale is described by a field $ϕ(x,t)$ that evolves by a Langevin equation that locally either conserves or not the field. Its dynamic behavior may also depend on the action of external agents on the bulk or/and at the system's boundaries. We derive the corresponding Fokker-Planck equation and the probability of a path and we use them to study general properties of the system's stationary state. In particular we focus on the study of the quasi-potential that defines the stationary distribution at the small noise limit. We argue that the system is at equilibrium when it is macroscopic reversible, that is when the most probable path to create a fluctuation from the stationary state is equal to the time reversed path that relaxes it. When this doesn't occur the system is in a nonequilibrium stationary state whose quasi-potential may present some lack of differentiability and/or long range action. We also derive closed equations for the two-body correlations at the stationary state and we apply them to some typical cases. Finally we obtain generalized Green-Kubo class of formulas by using the Large Deviation Principle.
