Although the final aim in the context of the VSC experiments is to provide a firm theoretical basis for cavity catalyzed reactivity in the collective regime, it is equally important to study single molecule systems since this would allow us to unambiguously identify and establish the need for a mechanism that is based on collective effects. At the same time, assessing whether the collective effect is purely quantum mechanical or not is also crucial, and hence requires both classical and quantum dynamical studies. Thus, for the paradigmatic model discussed above a question of interest to us is as follows. In the case of a one dimensional isomerization coordinate coupled to a lossless single cavity mode is it possible to rationalize the various observations of rate modulation within a purely classical phase space transport perspective? An example comes from the pioneering work of De Leon and Berne on a model isomerization system where it was noted that frequency variations have pronounced effects on the phase space of the system and hence on the onset of statisticality and the validity of linear rate laws. Another example comes from driven tunnelling models where detailed studies have established the interplay between classical phase space features and quantum coherence upon variation of the driving field frequency and strength. Both coherent destruction of tunneling and substantial enhancements of tunneling with variations in the frequency of the driving field have been predicted. In the context of rate theory in dissipative systems, we mention the work by Hershkovitz and Pollak showing the correlation between increasing energy loss, related to the depopulation factor in PGH theory, to enhanced chaoticity in the classical phase space. In general, as emphasized by Leitner and Gruebele , the effect of finite IVR rates combined with quantum localization effects can result in substantial deviations from the predictions of statistical theories. Therefore, we anticipate that similar dynamical effects must manifest in the cavity-system model and a classical-quantum correspondence based perspective for IVR dynamics can potentially yield useful mechanistic insights.