Breakdown of local equilibrium in coupled relaxation processes: Translational nonequilibrium during vibrational relaxation

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Abstract
Coupled relaxation processes involving several variables are examined using the theory of Markov Processes. This leads naturally to a relaxation equation for one of the variables which has the form of a master equation, but involves time dependent transition probabilities. The equation agrees with usual theories based on local equilibrium and time independent transition probabilities when both the correlations between the variables and the distribution function of the suppressed variables reach their equilibrium form more rapidly than the variable of interest. In order to test the relevance of deviations from local equilibrium, a model which mimics many of the properties of the coupled relaxation of translation and vibration for V−T energy exchange in a thermal reservoir is proposed and solved. Using cross sections which are like those for energy transfer in diatomic molecules, it is shown that important nonequilibrium correlations persist on the transient time scale of the relaxation of the translational degrees of freedom. These correlations can be large when the preponderance of molecules are initially in the ground state and are the order of magnitude of the enhancement of vibrational relaxation times observed at low temperatures.