Statistical Description of Fermi System over a Surface in a Uniform External Field

TL;DR

This paper develops a statistical framework for analyzing the thermodynamic properties of a Fermi system over a surface in a uniform external field, considering various conditions and field types.

Contribution

It introduces general formulas for thermodynamic quantities and density distribution of Fermi particles in a finite surface system under external fields.

Findings

Derived formulas for entropy, energy, and thermodynamic potential.

Calculated temperature dependence of heat capacities and density distribution.

Analyzed effects of gravitational and electric fields on the system.

Abstract

A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is assumed to be arbitrary, in particular, small. General formulas are obtained for entropy, energy, thermodynamic potential, heat capacities under various conditions and the distribution of the particle number density over the surface. In the continuum limit of a large surface area, the temperature dependences of heat capacities and density distribution are calculated. The cases of gravitational and electric fields are considered.