Instead of the transition rate for a configuration pair, it is more useful to obtain it for a state. From the definition of 𝜏(𝑣 ⃗), its value can only vary between zero and one, depending on the ratio between the thermal and the adiabatic transition event frequency. Therefore, I can define a function 𝜔(𝑞) which is smaller or equal to the degeneracy of the reactant or product state of the same energy level. 𝜔(𝑞) would represent the effective number of configurations where 𝜏(𝑣 ⃗) is one.