Asymptotic methods for confined fluids

TL;DR

This paper develops an asymptotic method to accurately transform grand-canonical ensemble results into the canonical ensemble for confined fluids, addressing unphysical artifacts and improving thermodynamic and microstructural descriptions.

Contribution

It introduces a contour integral approach in the complex fugacity plane to derive asymptotic expansions for the canonical partition function and density from grand-canonical data.

Findings

The method reveals the role of Yang-Lee zeros in ensemble transformations.

Numerical tests on a 1D hard-rod model validate the approach.

The approach improves the accuracy of confined fluid descriptions.

Abstract

The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can introduce unphysical artifacts. We employ the method of asymptotics to transform grand-canonical observables to the canonical ensemble, where the former can be conveniently obtained using the classical density functional theory of inhomogeneous fluids. By formulating the ensemble transformation as a contour integral in the complex fugacity plane we reveal the influence of the Yang-Lee zeros in determining the form and convergence properties of the asymptotic series. The theory is employed to develop expansions for the canonical partition function and the canonical one-body density. Numerical investigations are then performed using an exactly soluble one-dimensional model system of hard-rods.