The conventional books on thermodynamics that I know, do not talk about the thermodynamics of relativistic systems. But in Cosmology, the thermodynamic concepts are often applied to the whole universe.
My question is about the concept of thermodynamic equilibrium for a relativistic system consisting of electrons, positrons and photons. In this system, there are processes of the type $$e^++e^-\leftrightarrow \gamma+\gamma.$$ However, for chemical equilibrium, the forward reaction must proceed at the same rate as the backward reaction. Now, if the temperature (of the environment) falls below a certain value, photons will not have enough energy required for pair production. In particular, if the temperature is such that the average photon energy falls below the rest energy $2m_ec^2$ the backward reaction will stop.
Does it mean that the system fails to be in equilibrium below that critical temperature?
Since the forward reaction continues to occur, shouldn't the system ultimately equilibrate with only photons (that obey the blackbody distribution?).