  The non-equilibrium electron-positron-photon plasma thermalization process is
studied using relativistic Boltzmann solver, taking into account quantum
corrections both in non-relativistic and relativistic cases. Collision
integrals are computed from exact QED matrix elements for all binary and triple
interactions in the plasma. It is shown that in non-relativistic case
(temperatures $k_B T\leq 0.3 m_e c^2$) binary interaction rates dominate over
triple ones, resulting in establishment of the kinetic equilibrium prior to
final relaxation towards the thermal equilibrium, in agreement with the
previous studies. On the contrary, in relativistic case (final temperatures
$k_B T\geq 0.3 m_e c^2$) triple interaction rates are fast enough to prevent
the establishment of kinetic equilibrium. It is shown that thermalization
process strongly depends on quantum degeneracy in initial state, but does not
depend on plasma composition.
