Behavior of distribution functions in the thermodynamic limit

Abstract

Ruelle has proven that the solutions of the Kirkwood‐Salsburg equation for a finite volume Λ become, in the limit as Λ → ∞, the solutions to the Kirkwood‐Salsburg equation for an infinite volume, i.e., lim Λ→∞ ρ Λ →ρ+ lim Λ→∞ ε(Λ), lim Λ→∞ ε(Λ)→0 .The form of ε is not obtained. We show that for the first order contribution to the solution of the Kirkwood‐Salsburg equations obtained via a perturbation scheme developed in an earlier paper that ε(Λ)⩽ lim R→∞ ε −k′ a R ,where k′a is a positive real constant which can be specified and R is the minimum distance from the container walls to the particles of the system.