Thermodynamics of the electron-positron plasma at very high temperatures

TL;DR

This paper develops analytical formulas for the thermodynamic properties of high-temperature electron-positron plasmas, facilitating better understanding of their behavior in thermal equilibrium and ultra-relativistic regimes.

Contribution

It introduces a new series expansion method for Fermi-Dirac functions applicable to high-temperature electron-positron plasmas and related ultra-relativistic Fermi gases.

Findings

Formulas accurately describe thermodynamics at high temperatures

Series expansions depend explicitly on the μ/T ratio

Method applicable to thermal equilibrium and ultra-relativistic gases

Abstract

Thermodynamic properties of the electron-positron plasma (or gas) at high and very high temperatures are investigated. To achieve this goal we have derived a number of analytical formulas for the Fermi-Dirac distribution functions (or spectral functions) which can be applied to various Fermi gases in different cases. Almost all these formulas are represented in the form of series expansions. The coefficients in these expansions are the explicit and relatively simple functions of the $\frac{\mu}{T}$ ratio, where $T$ is the temperature and $\mu$ is the chemical potential of this Fermi system. Our new approach works very well for high temperature electron-positron plasma, which is in thermal equilibrium with the photon gas of annihilation $\gamma-$quanta, and for the model ultra-relativistic gas of fermions, where there is no radiation at all.