Exact single-exponential relaxation (ESER) of average energy (= the first moment of the population distribution) in a bulk system can be demonstrated only in the case of molecular models for the relaxing molecule that satisfy special conditions: a harmonic diatomic, or classical polyatomic. Yet experiment shows that single-exponential relaxation occurs in polyatomic molecules where such special conditions are unlikely to be met. This paper takes the view that if experimental error is taken into account, experiment can only demonstrate approximately exponential relaxation (AER) which is much less restrictive. It is shown that a useful criterion for ESER, closely related to experimental observables, is that the time correlation function for average energy transfer in the bulk system be a linear function of the time correlation function for average energy, with zero intercept, a condition that in AER need be satisfied only within experimental error. Examples are presented of simple transition probability models of a polyatomic molecule that meet these conditions. The most successful ones are based on a microcanonical argument, which suggests that the underlying cause of AER is near-ergodic behavior of the collision partners. Strong- and weak-collision-type energy transfer then depends on which degrees of freedom of the heat bath collision partner behave ergodically. © 1990.
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