Svante Arrhenius (1889) equation is often used to characterize the effect of temperature on the rates of chemical reactions. The Arrhenius formula gave a simple and powerful law, which in a vast generality of cases describes the dependence on absolute temperature   of the rate constant as following,
where    is the absolute temperature,  is the gas constant and the factor   varies only slightly with temperature. The meaning attached to the energy of activation   is as the minimum energy, which molecules need have to overcome the threshold to reaction. Therefore, the year 1889 can be considered as the birth date of reactive dynamics as the study of the motion of atoms and molecules in a reactive event. Eq. (1) was motivated by the 1884 discovery by vant Hoff   of the exponential dependence from the temperature of the equilibrium constants for most reactions: Eq.(1), when used for both a reaction and its inverse, agrees with vant Hoff's equation interpreting chemical equilibrium as dynamical at the microscopic level. In case of a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the activation energy and the pre-exponential factor can both be determined.
However, advances in experimental and theoretical methods have revealed the existence of deviation from Arrhenius behavior (Fig.1).
To overcome this problem, Aquilanti and Mundim proposed (2010) a generalized Arrhenius law based on algebraic deformation of the usual exponential function. Starting from the Euler exponential definition given by,
defining the deformed exponential function as,
Identifying the deformation parameter   as a continuous generalization of   . At the limit   the d-exponential function, , coincides with the usual exponential according to the well-known limit due to Euler, that is,
This definition was first used in thermodynamics and statistical mechanics by Landau. In the most recent scientific literature, there is a variety of deformed algebras with applications in different areas of science. Considering the d-exponential function, we introduce the deformed reaction rate coefficient, , in the following way,
and at the limit   the usual Arrhenius reaction law is recovered (Figs.1 and 1a).  is pre-exponential factor. Taking the logarithm of , Eq.(5), we obtain the following expression for the non-Arrhenius plot,
The logarithm of the reaction rate coefficient against reciprocal temperature shows a curvature, rather than the straight-line behavior described by the usual Arrhenius law (Figs.1 and 1a).
In Tolman’s definition the barrier or activation energy is a phenomenological quantity defined in terms of the slope of an Arrhenius law; it is usually assumed to be independent of absolute temperature (T), requires only local equilibrium and in general is given by
where  is constant and  is the ideal gas constant. 
To generalize Tolman´s definition, in the case chemical reactions, we assume that the barrier or activation energy is a function of the temperature given by the following differential equation,
  or   →     (8)
where   (constant) at limit    and the usual activation energy law is recovered as a constant. Noticeably, on the contrary of the usual Arrhenius case, the barrier or activation energy is temperature dependent and   has different concavities depending on the value of the d parameter (see Figs.1 and 1a). Thus, a positive convexity means that  decreases with increasing temperature. This general result is explained by a new Tolman-like interpretation of the activation energy through Eq.(8).
In the recent literature, it is possible to find different applications to verify the applicability of this new chemical reaction formalism