II. How does a magnon gas reach a statistical energy distribution?
In general an ideal gas is characterized as an ensemble of particles which interact with each other only through elastic scattering. And this is also the mechanism that maintains that any energy in an ideal gas is, within a defined time, distributed over all particles in such a way that the energy distribution follows one of the three statistical laws (Maxwell-Boltzmann; Fermi-Dirac or Bose-Einstein).
Like atoms in a classical atom gas, magnons in a magnon gas can also scatter with each other. In this way kinetic energy can be distributed over the whole magnon gas. The time scale for these scattering events between magnons depends on magnon density. This is plausible; the more particles are in a given volume, the higher the probability that two or more particles hit each other.
At sufficiently high magnon densities this time scale drops to the nanosecond regime. This is a thousand times faster than the interaction between spin and lattice vibrations. This means that magnons are able to "thermalize" before they dissipate into the lattice. Thermalization means the process of reaching a thermal energy distribution. This state is a different form of thermal equilibrium, a so called Quasi-Equilibrium. The next section will treat the question: