It is shown, that by means of a special projection operator, the Liouville equation for an $N$-particle distribution function of classical particles, driven from an equilibrium state by an external field, can be exactly converted into a closed linear homogeneous Generalized Master Equations (GMEs) for an $s$-particle ($s<N$) distribution function. The obtained linear time-convolution and time-convolutionless GMEs define a subdynamics in the $s$-particle phase space and contains no inhomogeneous initial correlations terms as compared to the conventional GMEs. No approximation like ”molecular chaos” or Bogoliubov’s principle of weakening of initial correlations is needed. The initial correlations are ”hidden” in the projection operator and thus they are accounted for in the obtained equations. For the weak interparticle interaction and weak external field, these equations are rewritten in the second order of the perturbation theory. Essentially, that they contain the contribution of initial correlations in the kernel governing the evolution of an $s$-particle distribution function. In particular, the evolution equation for a one-particle distribution function is obtained and its connection to the nonlinear Landau and the Fokker–Planck equations is discussed. The obtained results are related to the general issues of statistical physics and to the physical applications (plasma physics).

结果表明，借助特殊的投影算子，Liouville方程 $ñ$由外部场从平衡状态驱动的经典粒子的粒子分布函数可以精确地转换为一个封闭的线性齐次广义主方程（GME） $s$-粒子（$s<ñ$） 分配功能。所获得的线性时间卷积和无时间卷积GME定义了$s$-粒子相空间，与常规GME相比，不包含任何不均匀的初始相关项。不需要像“分子混乱”或Bogoliubov减弱初始相关性的原理这样的近似方法。初始相关在投影算子中被“隐藏”，因此它们在获得的方程式中得到考虑。对于弱的粒子间相互作用和弱的外部场，这些方程式按扰动理论的第二阶重写。从本质上讲，它们包含控制内核演化的内核中的初始相关性的贡献。$s$-粒子分布函数。特别是，获得了单粒子分布函数的演化方程，并讨论了其与非线性Landau方程和Fokker-Planck方程的关系。获得的结果与统计物理学的一般问题和物理应用（等离子物理学）有关。