布朗粒子的动量关联函数是非平衡统计力学的一个极为重要的物理量，然而国内常用教材对其及相关内容的讲解存在瑕疵.本文从学术研究的角度，对有关动量关联函数的一些不严谨表述进行了厘清.目前的非平衡统计教学皆以含白噪声的朗之万方程为模型，但很难明晰布朗运动中的两个特征时间: 涨落力关联时间和系统驰豫时间.本文以Ornstein-Uhlenbeck色噪声驱动的广义朗之万方程为例解决了这一问题.还讨论了判断各态历经变量的Khinchin 定理，进而深化了动量关联函数的价值.

The momentum correlation functuin is a very important physical quantity in non-equilibrium statistical mechanics.However，where are a few errors for the explain of this function and related contents in our usual textbooks.This paper starts from academic research and discusses those un-rigorous descriptions.The Langevin equation subjected to a white noise is regarded as a model in the present textbooks，but it is difficulty for clearing two characteristic times in the Brownian motion: the correlation time of random force and relaxation time of system.This paper solves this question in terms of the generalized Langevin equation with an Ornstein-Uhlenbeck colored noise. The ergodicity of the momentum variable is studied by using the Khinchin theorem and thus the cost of the momentum correlation function is deepen.