On the reduction of many‐body dielectric theories to the Onsager equation

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Abstract
An approximate theory for the dielectric constant ε of a dense polar fluid was derived by Ramshaw, Schaefer, Waugh, and Deutch (RSWD). In the present article, the RSWD theory is generalized and made rigorous by another method of derivation. The result is a rigorous expression for ε which differs from the RSWD expression by the presence of a fluctuation term. Both the rigorous expression and the RSWD expression are then specialized to the Onsager model. It is found that the rigorous expression for ε reduces to the Onsager equation, but that the RSWD expression does not because the fluctuation term is nonzero (and nonnegligible) for the Onsager model. The well‐known discrepancy between the Onsager equation and the theory of Harris and Alder is found to have the same origin.

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