The commutative property of strong-transition rate matrices

Abstract

The (n − 1)-fold degenerate set of transition probabilities used in our recent reformulation of unimolecular reaction theory is operationally equivalent to the set of effective strong-transition probabilities introduced recently by Nordholm. We have found that the relaxation matrix corresponding to these transition probabilities commutes with any other relaxation matrix which will drive the same system to a Boltzmann distribution at infinite time. Some useful results stemming from this commutative property are presented; we expect that these results will help to clarify further the nature of the assumptions underlying strong- and effective strong-collision theories.