Evolution of Reduced Distribution Functions. III. General Truncation and Solution of the Linearized Classical BBGYK Hierarchy

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Abstract
A linearized version of the nonequilibrium BBGYK hierarchy applicable to simple fluid systems near equilibrium is derived. A sequence of successive extended dynamical superposition approximations is defined to truncate the hierarchy at any arbitrary level. A formal solution, applicable either to the truncated or the complete hierarchy, is obtained by iteration of the Laplace transformed hierarchy followed by inversion of the transform. For the lowest truncation, which produces a single kinetic equation for the one‐body reduced distribution function, the Fourier–Laplace transform of the solution is summed to a closed form.