Surface in statistical ensembles

TL;DR

This paper investigates surface terms in various statistical ensembles, revealing their roles in closed and open systems, and relates surface particles to density oscillations and surface tension at boundaries.

Contribution

It demonstrates that all studied ensembles include surface terms, clarifies their physical interpretation, and extends understanding of surface effects in statistical mechanics.

Findings

Surface terms are present in all studied ensembles.

Surface particles relate to density oscillations near boundaries.

Surface effects are consistent with surface tension concepts.

Abstract

The present contribution deals with surface terms appearing immediately in distributions and partition functions of statistical ensembles. It is shown that all ensembles under study, including ordinary canonical and grand canonical ensembles, involve surface terms. For a canonical ensemble both surface and volume terms correspond to a closed system. For a grand canonical ensemble the volume term corresponds to an open system, while the surface one - to a closed one. Finally, for the recently introduced open statistical ensemble the specific feature of which is the consideration of some surrounding region both volume and surface terms correspond to an open system. In conclusion, surface particles at solid/fluid boundary are interpreted as particles corresponding to number density oscillations near the surface; this completely agrees with the earlier introduced concept of surface tension at such a boundary.