Two approximations for the classical triplet distribution function

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Abstract
Two approximations are proposed for the triplet distribution function in classical fluids in the form of infinite series expansions. When used together with the second equation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, the first approximation is shown to yield precisely the pair distribution function in the hypernetted-chain (HNC) approximation, while the second approximation gives the pair distribution function in the Percus-Yevick (PY) approximation. Both approximations are applied to non-equilibrium systems near equilibrium. As an example, application to the calculation of transport processes in electrolyte solutions is considered. The infinite series expansions are summed to give closed integral equations for the triplet distribution function that are related to the HNC and PY integral equations for the binary distribution function.