Construction of equations for classical equilibrium correlation Green's functions on the basis of kinetic equations. I

Equations for equilibrium correlation Green's functions are constructed in the framework of the general theory developed by the author [1] on the basis of various kinetic equations for single-component classical systems. The following kinetic equations are used: (Markov) Fokker–Planck, Boltzmann–Lorentz, Enskog–Lorentz (for Brownian particles), Vlasov–Landau, Boltzmann, Boltzmann–Enskog, Enskog, Rice–Allnatt, and a model kinetic equation and the (non-Markov) Vlasov–Landau equation. For systems of Brownian particles expressions are found (in the 13- and 14-moment approximations) for the density-density equilibrium correlation Green's functions, etc.