Equilibrium states of a new kinetic equation

We start with a recently proposed kinetic equation describing the time evolution of a gas of two level atoms. In this model, an atom in any of the two states may radiate energy by giving up some of its kinetic energy. The transition rates from any of the two states to the other are now assumed equal, simplifying all our previous results. With this assumption, we finally find equilibrium states of the resulting kinetic equation. The equilibrium states are not unique, nor Maxwellian, yielding thermodynamic properties which may be of some applicability to the phenomenon of turbulence.