Examples of the construction of integral equations in equilibrium statistical mechanics from invariance principles

Ronald Lovett and Frank P. Buff

Physica A: Statistical Mechanics and its Applications, 1991, vol. 172, issue 1, 147-160

Abstract: The integral equation which identically relates the gradient of the density ▿ϱ(r) and the Ornstein-Zernike direction correlation function c(r.r′) is derived from a simple but fundamental invariance principle. This generalization of the heuristic translational invariance argument used in the past establishes that this integral equation is valid even in the presence of intermolecular forces which are not translationally invariant. The same methodology can be used to generate all the integral equations in the hierarchy of relations between ▿ϱ(r) and higher-order direct correlation functions. It is also observed that, as one can proceed up the hierarchy by simple functional differentiation, it is also possible to proceed down the hierarchy. In particular, the generation of the first member of the hierarchy from the second provides a derivation of this relation which closely parallels the derivation of the first member of the Born-Green-Yvon hierarchy. The hierarchy of integral equations based upon rotational invariance is similarly developed.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:172:y:1991:i:1:p:147-160

DOI: 10.1016/0378-4371(91)90317-6

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