Thermodynamics of the Relativistic Fermi gas in D Dimensions

TL;DR

This paper investigates how spatial dimensions and particle-antiparticle pair production influence the thermodynamic behavior of the relativistic Fermi gas, revealing phase transition-like features and estimating critical temperatures relevant to quark-gluon plasma.

Contribution

It provides a detailed analysis of the thermodynamics of the relativistic Fermi gas across dimensions, highlighting phase transition phenomena and estimating critical temperatures for high-energy systems.

Findings

Identification of a minimum in isothermal compressibility at a characteristic temperature.

Observation of a phase transition-like behavior in thermodynamic susceptibilities.

Estimation of the critical temperature for quark-gluon plasma formation.

Abstract

The influence of spatial dimensionality and particle-antiparticle pair production on the thermodynamic properties of the relativistic Fermi gas, at finite chemical potential, is studied. Resembling a kind of phase transition, qualitatively different behaviors of the thermodynamic susceptibilities, namely the isothermal compressibility and the specific heat, are markedly observed at different temperature regimes as function of the system dimensionality and of the rest mass of the particles. A minimum in the isothermal compressibility marks a characteristic temperature, in the range of tenths of the Fermi temperature, at which the system transit from a normal phase, to a phase where the gas compressibility grows as a power law of the temperature. Curiously, we find that for a particle density of a few times the density of nuclear matter, and rest masses of the order of 10 MeV, the minimum of the compressibility occurs at approximately 170 MeV/k, which roughly estimates the critical temperature of hot fermions as those occurring in the gluon-quark plasma phase transition.