Title: Universal Form of Stochastic Evolution for Slow Variables in Equilibrium Systems Show Chinese title

Title: 平衡系统中慢变量的随机演化通用形式

Abstract: Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that obtained by Green. An equation with a nonlinear friction term for Brownian motion turns out to be an example of the general results. A key method in our derivation is to use different discretization schemes in a path integral formulation and the corresponding Langevin equation, which also leads to a consistent understanding of apparently different expressions for the path integral in previous studies. Show Chinese abstract

Abstract: 非平衡系统中一组完整的慢变量的非线性乘法朗之万方程通常是基于时间尺度分离原理推导出来的。 这些方程的形式是普遍的，等同于格林所得出的结果。 一个带有非线性摩擦项的布朗运动方程被证明是普遍结果的一个例子。 我们推导中的关键方法是在路径积分公式和相应的朗之万方程中使用不同的离散化方案，这也有助于对先前研究中路径积分的不同表达式达成一致的理解。