  When the temperature of a trapped Bose gas is below the Bose-Einstein
transition temperature and above absolute zero, the gas is composed of two
distinct components: the Bose-Einstein condensate and the cloud of thermal
excitations. The dynamics of the excitations can be described by quantum
Boltzmann models. We establish a connection between quantum Boltzmann models
and chemical reaction networks. We prove that the discrete differential
equations for these quantum Boltzmann models converge to an equilibrium point.
Moreover, this point is unique for all initial conditions that satisfy the same
conservation laws. In the proof, we then employ a toric dynamical system
approach, similar to the one used to prove the global attractor conjecture, to
study the convergence to equilibrium of quantum kinetic equations, derived in
[49,50].
