On the Kirkwood-Salsburg and Mayer-Montroll equations and their solutions for many-body interactions

H. Moraal

Physica A: Statistical Mechanics and its Applications, 1981, vol. 105, issue 1, 286-296

Abstract: The Kirkwood-Salsburg and the Mayer-Montroll equations for an arbitrary stable interaction are derived for the case of an exponentially integrable external potential (of which a finite volume is a special case). It is shown that the Mayer-Montroll equation has at least one solution (the equilibrium state) if the activity z is such that the grand canonical partition function Ξ(z) is nonzero; also, there is at least one eigenvector with eigenvalue 1 for z such that Ξ(z) = 0. The difference with the Kirkwood-Salsburg equation lies in the possibility of more solutions, as is shown by an example.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:105:y:1981:i:1:p:286-296

DOI: 10.1016/0378-4371(81)90077-7

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