Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a “d-TST” formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto–Tsallis statistical weights: these generalize the Boltzmann–Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super -Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub -Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti -Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’.