Equation of state of the relativistic electron–positron–photon plasma at arbitrary temperature and degeneracy

We consider the plasma made of relativistic electrons and positrons in thermodynamic equilibrium with photons at arbitrary temperature and degeneracy. We establish various thermodynamic identities as a function of the electron and positron chemical potentials and temperature. The high-temperature regime in which the electrons and positrons are ultrarelativistic is recovered. The excess of electrons with respect to positrons or the excess of positrons with respect to electrons depends on the thermodynamic conditions. Doing so, we go beyond what is usually found in the literature where only the high temperature regime is usually tackled.