## 1 Introduction
### Outline of the Problem  
Taking the most general course of consideration according to [4], the mentioned effects can be presented in the form of Equations (1)-(3) for \(\beta\), \(\gamma=\text{const}\):  
\[\ln A_{i}= \gamma+\frac{E_{i}}{R\beta} \tag{1}\] \[\Delta H_{i}^{+}= \gamma+\beta\Delta S_{i}^{+} \tag{2}\]or  
\[\Delta H_{i}^{\varnothing}=\gamma+\beta\Delta S_{i}^{\varnothing} \tag{3}\]  
In Equations (1)-(3), the \(\beta\) symbol stands for \(T_{iso}\) (Equation (1)) and \(T_{c}\) (Equations (2) and (3)) suggesting that these are the same temperatures in a value sense. Provided between Equations (1) and (2) there are approximate, although reliable relationships, the reference of the same equations to thermodynamic standard functions is not obvious. The formal notation of Equation (3) has been demonstrated for many chemical, biochemical or physicochemical reactions/processes [1; 4; 5; 6; 7; 8; 9].  
In the Gold Book [10] Equation (2) is presented as isokinetic relationship:  
\[\Delta H_{i}^{+}-\beta\Delta S_{i}^{+}=\text{const} \tag{4}\]  
and Equation (3) is related to chemical reaction as the isoequilibrium relationship:  
\[\Delta_{r}H-\beta\Delta_{r}S=\text{const} \tag{5}\]  
Equations (4) and (5) and also (1) express the view of [PERSON] [3], who (briefly) postulates that the compensation or isokinetic temperature is determined by the identity of the chemical equilibrium constants or kinetic constants, respectively. In the first case, van't Hoff's isobar together with the Gibbs free energy is used in the proof and reduced to \(EEC\), and the second is commonly known and accepted as \(KCE\), and is related to the Arrhenius equation.  
By way of theoretical considerations, [PERSON] proved the validity of Equation (3) based on Bayesian statistical mechanics [11]. Equations (2) and (4) contain thermodynamic activation functions derived from [PERSON]'s theory from 1935 [12]. The theory has been adapted for modeling complex reaction/process pathways, as well as for the practical use of selected relationships captured by Equations (2)-(5) [1; 3; 5; 8; 9; 13; 14; 15; 16; 17; 18; 19; 20]. Some of the mentioned works combine [PERSON]'s theory with the Arrhenius equation [13; 14; 18].  
Analyzing the experimental data obtained under isothermal and dynamic conditions, a large discrepancy in the values of determined isokinetic temperatures can be observed. The application of isothermal, dynamic or isoconversional kinetic functions for modeling does not lead to one common isokinetic temperature value [20]. Thus, it can be expected that the reliability of Equation (2) or Equation (4) is dependent on the parameters determined from kinetic equations or reduced to thermokinetics, consistent with the classical Arrhenius equation, i.e., In \(A\) vs. \(E\). Consequently, the possibility of confronting the isoconversion and compensation temperature relationships arises.  
In this type of analysis, temperatures defining the initial temperature [21] or [22] and isokinetic are still useful. The equilibrium temperature follows from Equation (5) when we introduce \(\text{const}=0\), i.e.,  
\[T_{eq}=\frac{\Delta_{r}H^{\varnothing}}{\Delta_{r}S^{\varnothing}}\text{ when }\Delta_{r}G^{\varnothing}=0 \tag{6}\]  
In this work, an attempt is made to use the isokinetic \((T_{iso})\) and compensation \((T_{c})\) temperatures as quantities representative for considered kinetic functions \(f(\alpha)\) to demonstrate isokinetics, which is largely understood as the closeness of the Arrhenius law parameter values determined by the known equations.