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A variational approach to distribution function theory

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Abstract

We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at theKth term and minimization of the resulting approximation leads to equations for the distribution functions up toKth order.

The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one.

The conceptual approach is adapted from the cluster variation method of lattice theory.

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Authors and Affiliations

  1. Koninklijke/Shell Exploratie en Produktie Laboratorium, P.O. Box 60, 2280 AB, Rijswijk, The Netherlands

    Antoine G. Schlijper

  2. Department of Materials Science and Engineering, University of California at Los Angeles, 90024, Los Angeles, California

    Ryoichi Kikuchi

Authors
  1. Antoine G. Schlijper
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  2. Ryoichi Kikuchi
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Schlijper, A.G., Kikuchi, R. A variational approach to distribution function theory. J Stat Phys 61, 143–160 (1990). https://doi.org/10.1007/BF01013957

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  • DOI: https://doi.org/10.1007/BF01013957

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