  Electron-positron annihilation largely occurs in local thermal and chemical
equilibrium after the neutrinos fall out of thermal equilibrium and during the
Big Bang Nucleosynthesis (BBN) epoch. The effects of this process are evident
in BBN yields as well as the relativistic degrees of freedom. We
self-consistently calculate the collision integral for electron-positron
creation and annihilation using the Klein-Nishina amplitude and appropriate
statistical factors for Fermi-blocking and Bose-enhancement. Our calculations
suggest that this annihilation freezes out when the
photon-electron-positron-baryon plasma temperature is approximately 16 keV,
after which its rate drops below the Hubble rate. In the temperature regime
near 16 keV, we break the assumption of chemical equilibrium between the
electrons, positrons, and photons to independently calculate the evolution of
the chemical potentials of the electrons and positrons while computing the
associated collision integrals at every time step. We find that the electron
and positron chemical potentials deviate from the case with chemical
equilibrium. While our results do not affect the interpretation of precision
cosmological measurements in elucidating the standard cosmological model, these
out of equilibrium effects may be important for testing physics beyond the
standard model.
