A physical system is in thermodynamic equilibrium if its energy is distributed evenly among all the different ways in which its components can move or vibrate – what physicists call the system’s “degrees of freedom” – and there is no flow of energy within or at the boundaries of the system. The average energy per degree of freedom is a direct measure of the system’s temperature.
The totality of all electromagnetic fields is a physical system as well. More information about how thermal equilibrium of a hot body and the electromagnetic fields leads to the emission of thermal radiation can be found in the spotlight text Heat that meets the eye.
The situation is slightly more complicated in systems that allows transmutations – for instance a system consisting of particles of species A and particles of another species B, where A-particles can change into B-particles and the other way around, For such a system, equilibrium at a certain temperature implies definite values for the relative abundances of the different particle species – how many particles of species A there should be, on average, for each particle of another species B. Such equilibria are of great importance for the physics of the early universe, as described by the big bang models.