On the Consistency of the Yvon–Born–Green Hierarchy and Its Truncations

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Abstract
The assumption of truncation of the hierarchy of reduced distributions for fluids at thermodynamic equilibrium is discussed. We consider the question of whether a truncated hierarchy yields expressions for the mean force on a molecule, in the presence of its neighbors, which are conservative. It is concluded that in general it does not, although the Kirkwood superposition and the infinite hierarchy do. The conclusion is reached that, unless the closure satisfies a certain condition, the truncated hierarchy in general has no solutions.

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