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

Abstract

We considered a model of a small system with internal particles and surface degrees of freedom. All the main statistical distributions were obtained explicitly on a pre-thermodynamic limit basis. The concept of temperature or thermodynamic equations was not used. The distribution of the coordinates of a surface element allows for the rigorous determination of the pressure exerted by the internal particles. In this way, we have derived the exact equation of state for a small system with a surface. It relates the pressure to the numbers of bulk and surface degrees of freedom, their mean energies, and other parameters. 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, it transfers to the usual equation of state for an ideal gas.