The classical fluctuation model for inelastic collisional interactions - I : Theory

Using an analogy with Statistical Thermodynamics and the Einstein equation for fluctuation probabilities a “fluctuation” model for the inelastic collisional interaction governing molecular energy transfers is introduced. Symmetrized expressions respecting the detailed balance principle are obtained for the classical and semiclassical transition probabilities and are shown to be equal – within standard approximations (saddle-point for perturbation integrals) – to the corresponding quantum mechanical WKB equations. Rules are stated, useful to transform classical results into quantum mechanical WKB results. Although introduced for the case of vibration-translation molecular energy transfers the model equations reveal some generality and can be applied to a number of inelastic processes in physics. The “continuum” and “discrete” theoretical cases are discussed together with a few possible developments.