A new statistical mechanical formalism for gases

TL;DR

This paper introduces a novel statistical mechanical formalism for gases that unifies thermodynamics and microstructure analysis, with applications to astrophysical atmospheres and ionized hydrogen gases.

Contribution

It develops a new equilibrium theory based on space distribution among particles, providing both thermodynamic and structural insights in a unified framework.

Findings

Derived equations of state and distribution functions in multiple dimensions.

Applied formalism to describe atomic populations in ionized hydrogen gas.

Enabled detailed evaluation of atomic density and internal states.

Abstract

An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties in atmospheres of degenerate stars. Present paper focuses on diluted one-component systems, where the interaction energy is calculated as a sum of binary contributions. The spatial configuration of the gas is described in terms of a particle-state variable v which roughly measures the free space surrounding each particle. The formalism offers a unified treatment of both thermodynamics and structure of fluids, since it not only provides the state function (the Helmholtz free energy) of a fluid, but also automatically gives information on the microstructure of the system (e.g. the nearest-neighbor distribution function). Equations of state and nearest-neighbor distribution functions of perfect and hard-body fluids are obtained in straightforward way in one, two and three dimensions. The formalism is applied to describe the atomic population in a partially ionized hydrogen gas. Combined and self-consistent evaluations of atomic populations and internal effects on bound states are performed in a detailed form. The present theory allow us to resolve the atomic density at each internal level into groups of atoms which experiment different perturbation intensities according to the size of their spaces v.