We exploit the accuracy and computational speed of the angular momentum model of inelastic transfer to follow changes in quantum state populations as a gas ensemble evolves from an initial state of dis-equilibrium. Results on two prototype systems in specific initial states are presented and the manner by which these approach equilibrium is discussed. There are wide differences in the rates at which different internal modes equilibrate and although Boltzmann-type distributions are found within a mode, individual modes may not be in equilibrium with one another. These findings have relevance, e.g., to upper atmosphere modeling where the rapid establishment of local thermodynamic equilibrium is often assumed
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