Subdynamics of a many-particle classical system driven from an equilibrium state by an external force

Abstract

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).