can be considered as temperature dependent. It was postulated as the basic expansion the reciprocal-activation reciprocal-temperature relationship, for which can provide a formal mathematical justification by Tolman Theorem. The  function  when written as the logarithmic derivative of the rate constants with respect to ,  Eq. (7), the concept to an activation energy represents an energetic obstacle to the progress of the reaction: therefore its reciprocal can be interpreted as a measure of the propensity for the reaction to proceed and defined as the specific transitivity  () of the process:
This notation emphasizes the fact that in general the transitivity can take a gamma of values, but not including abrupt changes e.g. in the mechanism or in the phases of reactants. If it is admit a Laurent expansion in  a neighbourhood around a reference value, it is possible recover the Eqs. (6) and (8).
What it is call the sub-Arrhenius behaviour would be accounted for traditionally by introducing a tunnelling parameter () in the conventional Transition-State-Theory. In the -TST formulation, it is replace the factor  in the TST rate constant by the deformed exponential function, Eq. (3), yielding:
where  is Planck constant, is Boltzmann constant  and   is the (translational, vibrational and rotational) partition functions of the reactants, and is the partition function of the activated complex. In Ref., the significance of the  parameter  and an explicit procedure for its calculation were  proposed, which it is inversely proportional to the square of the barrier height  ()and directly proportional to the square of the frequency for crossing the barrier  () at a saddle point in the potential energy surface: