## 1 Introduction
Empirical formulations first emerged, and then they were followed by many authors attempting to use statistical physics theory to justify the form of the empirical laws previously found [11]. These studies drew a parallel between gas phase and solid phase kinetics. Dating to the middle of the 20 th-century, several authors questioned the form of the statistical distributions when applied to the reactions resulting in the thermal degradation of solids [12; 13]. Among the different approaches, the most common one establishes that for a non-oxidative degradation reaction, the production rate (\(r\)) is given by:  
\[r=\bigg{(}\frac{\rho_{s}}{\rho_{s}(0)}\bigg{)}^{n_{s}}A^{pf}e^{-\frac{E_{act}} {RT}} \tag{2}\]  
where \(n_{s}\) represents the reaction order, \(A^{pf}\) the pre-exponential factor, \(E_{act}\) the activation energy, \(R\) the perfect gas constant and \(T\) the temperature. Then, Equation (2) is composed of the quantity of reactive mass (\(\bigg{(}\frac{\rho_{s}}{\rho_{s}(0)}\bigg{)}^{n_{s}}\)) and the reaction rate relation (\(A^{pf}e^{-\frac{E_{act}}{RT}}\)). This last relation is known as the Arrhenius relation, first established in 1889 by [PERSON] [10]. All the current models [5; 6; 7; 8] have their own representations of the transport equations consistent with conventional conservation equations [4]. While each author prioritizes specific phenomena relevant to the processes they intend to model, they adopt different simplifications and choose different expressions to model individual phenomena. The same relation (Arrhenius form) is used in all solid degradation models [13; 14; 15]. Most studies concerned with thermal degradation of solids have not been devoted to formulation itself, but to better understand the input parameters (pre-exponential or the activation energy), to find optimized methodologies to extract these parameters from data, to establish the mechanisms by which fuel is produced and transported (\(n\)th order, diffusion...) and to describe the influence of temperature on the different parameters [15]. A detailed example of such studies is reference [16], where it is clearly established that the form of the reaction rate expressions needs to be significantly modified when applied to different materials, many of relevant to fire safety. It is, therefore, clear that there is great confidence in the capacity of the Arrhenius representation to describe the thermal degradation of solids. Despite this confidence, there is almost no work that serves to unequivocally establish the theoretical underpinnings of the Arrhenius relation. The work of [PERSON] and [PERSON] [17] is one the most extensive study devoted to the theory underpinning the Arrhenius relation. While the authors conclude that such a model is inapplicable to the immobilized constituents of a solid, they also indicate that the energy distribution functions at the interface (where reactions occur) are analogous to those in the Maxwell-Boltzmann distribution functions used to justify using Arrhenius for gas-phase reactions. While important, this study focuses on degradation occurring as a single step in an infinitesimally thin interface and, therefore, is not conclusive as support to the wide range of applications of the Arrhenius relation in fire modeling. Consequently, this article is focused on the Arrhenius relation itself. The objective is to review the basis for the reaction rate relation used for solid degradation and to provide any available justification for selecting any specific form of this formulation. This paper is not intended to prove or disproof the validity of such a relation. Instead, it is directed to organize existing evidence so that those using these expressions in fire modeling can indicate the level of confidence behind the expression.