Open statistical ensemble and surface phenomena

TL;DR

This paper introduces a new open statistical ensemble considering surface effects in a one-component system, highlighting the importance of surface tension and adsorption phenomena at boundaries, with novel mathematical tools for thermodynamic relations.

Contribution

It proposes a new open ensemble framework that incorporates surface phenomena and employs recurrence relations and generating functions for thermodynamic calculations.

Findings

Surface tension depends on pressure and temperature, unlike in two-phase systems.

Surface effects are significant even in uniform media, affecting thermodynamic properties.

New mathematical methods improve the analysis of surface phenomena in statistical mechanics.

Abstract

In the present work we investigate a new statistical ensemble, which seems logical to be entitled the open one, for the case of a one-component system of ordinary particles. Its peculiarity is in complementing the consideration of a system with the inclusion of a certain surrounding area. The calculations indicate the necessity of taking into account the surface that delimits a given system even in the case when the latter is a part of a uniform medium and is not singled out one way or another. The surface tension coefficient behaves unlike two-phase systems in equilibrium and depends on two variables - pressure as well as temperature - and belongs to the boundary separating a hard solid from a fluid. As for the mathematical mechanism ensuring the fulfillment of thermodynamic relations, the emphasis is shifted from operating with series, like in the grand canonical ensemble, towards employing the recurrence relations of a new class of functions that incorporate Boltzmann and Ursell factors as their extreme cases and towards utilizing generating functions. The second topic of discussion that the present article deals with is the consideration of the surface tension and adsorption observed at the boundary of a solid body and a liquid or gas carried out on the basis of the analysis of the classical system found in a field of force of general type. The surface terms are calculated with the aid of field functions and the correlation functions of an unperturbed volume phase and behave somewhat vaguely; particularly, as a function of activity, they may start with a linear or quadratic term.