Thermodynamics of the nonrelativistic free-electron Fermi gas in one, two, and three dimensions from the degenerate to the nondegenerate temperature regime

TL;DR

This paper provides a comprehensive analysis of the thermodynamic properties of nonrelativistic free-electron Fermi gases across one, two, and three dimensions, covering the entire temperature range from degenerate to nondegenerate regimes.

Contribution

It offers new solutions for temperature-dependent properties in different dimensions, including detailed crossovers between degenerate and nondegenerate regimes.

Findings

Dimension-dependent thermodynamic property crossovers

Temperature dependence of chemical potential and internal energy

Graphical illustrations of property transitions

Abstract

The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the low- and high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat capacity at constant pressure, isothermal compressibility, and thermal expansion coefficient versus temperature in 2D and 3D. Of primary interest here are the detailed dimension-dependent crossovers of these properties between the degenerate and nondegenerate temperature regime, which are graphically illustrated for each of the above properties.