Equation of state of a small system with surface degrees of freedom

TL;DR

This paper derives an equation of state for a small finite system with surface degrees of freedom without relying on thermodynamic concepts, explicitly relating pressure to surface and bulk properties.

Contribution

It introduces a novel statistical model for small systems with surface effects, deriving an explicit equation of state without thermodynamic assumptions.

Findings

Pressure depends on bulk and surface degrees of freedom.

Surface potential energy exceeds kinetic energy per degree of freedom.

Equation of state reduces to ideal gas law in the thermodynamic limit.

Abstract

We have considered a model of a small finite system with internal particles and surface degrees of freedom. All the main statistical distributions were explicitly obtained, on a pre thermodynamic limit basis. The concept of temperature or any thermodynamic equations was not used. The distribution of coordinates of a surface element allows the rigorous determination of the pressure exerted by the internal particles. In this way, we have derived the equation of state for a small system with surface. It relates the pressure to the numbers of bulk and surface degrees of freedom, their mean energies and the volume. The mean potential energy of the surface was found to be higher than the mean kinetic energy, per degree of freedom. The obtained equation of state accounts for the influence of this excessive surface energy. In the thermodynamic limit, the temperature appears and the obtained equation of state transfers to the usual ideal gas one.