Derivation of Kinetic Equations from the Generalized Langevin Equation

Abstract

The projection operator techniques of Zwanzig and Mori are used to obtain a generalized Langevin equation describing the time evolution of the fluctuation of the microscopic phase density $\delta g(\overrightarrow{\mathrm{x}},\overrightarrow{\mathrm{p}},t)\equiv g(\overrightarrow{\mathrm{x}},\overrightarrow{\mathrm{p}},t)-〈g(\overrightarrow{\mathrm{x}},\overrightarrow{\mathrm{p}},t)〉$