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Formal Solution of the Equations of Statistical Equilibrium
1.J. Yvon, “La théorie statistique des fluides et l’equation d’état,” Actualitées sci. et ind. No. 203 (1935).
2.J. G. Kirkwood and E. Monroe Boggs, J. Chem. Phys. 9, 514 (1941);
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2.J. G. Kirkwood and E. Monroe Boggs, 10, 394 (1942)., J. Chem. Phys.
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6.J. G. Kirkwood, 15, 72 (1947); and later papers., J. Chem. Phys.
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8.Equations of the type of (6) have been considered, e.g., by Bazarov, J. Exptl. Theoret. Phys. U.S.S.R. 32, 1065 (1957),
8.translation: Bazarov, Soviet Phys. 5, 872 (1957).
9.Here and in the following we shall simply denote by a superscript zero quantities referring to the zero density limit. They will be related to each other by equations similar to those relating the corresponding quantities without superscript. Thus one has, together with Eqs. (10) and (12), the equations , . Quantities with a superscript zero are considered known.
10.The connection between equations like (10) and (11) has been pointed out before by Mazo and Zemach [Phys. Rev. 109, 1564 (1958)]. These authors also show how Eq. (10) can be used to prove quite simply the property of the functions of vanishing for large separation of the arguments, when the functions factorize for large separation.
11.See, D. ter Haar, Elements of Statistical Mechanics (Rhinehart and Company, Inc., New York, 1954).
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