Review The Basic Theorem of Temperature-Dependent Processes Valentin N. Sapunov 1, * , Eugene A. Saveljev 1 , Mikhail S. Voronov 1 , Markus Valtiner 2, * and Wolfgang Linert 2, *   Citation: Sapunov, V.N.; Saveljev, E.A.; Voronov, M.S.; Valtiner, M.; Linert, W. The Basic Theorem of Temperature-Dependent Processes. Thermo 2021, 1, 45–60. https:// doi.org/10.3390/thermo1010004 Academic Editor: Johan Jacquemin Received: 26 January 2021 Accepted: 23 February 2021 Published: 19 March 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Chemical Technology of Basic Organic and Petrochemical Synthesis, Mendeleev University of Chemical Technology of Russia, Miusskaya sq. 9, 125047 Moscow, Russia; savevgenii@gmail.com (E.A.S.); voronoff@muctr.ru (M.S.V.) 2 Department of Applied Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/134-AIP, 1040 Vienna, Austria * Correspondence: Sapunovvals@gmail.com(V.N.S.); valtiner@iap.tuwien.ac.at (M.V.); wolfgang.linert@tuwien.ac.at (W.L.) Abstract: The basic theorem of isokinetic relationships is formulated as “if there exists a linear correlation “structure∼properties” at two temperatures, the point of their intersection will be a common point for the same correlation at other temperatures, until the Arrhenius law is violated”. The theorem is valid in various regions of thermally activated processes, in which only one parameter changes. A detailed examination of the consequences of this theorem showed that it is easy to formulate a number of empirical regularities known as the “kinetic compensation effect”, the well- known formula of the Meyer–Neldel rule, or the so-called concept of “multi-excitation entropy”. In a series of similar processes, we examined the effect of different variable parameters of the process on the free energy of activation, and we discuss possible applications. Keywords: isokinetic relationship; Meyer–Neldel; multi-excitation entropy; free energy of activation 1. Introduction Exponential models of the temperature dependence of the properties of certain pro- cesses appeared in the scientific literature as early as the end of the 19th century. Such a functional dependence was proposed by Reynolds (1884) to describe the change in viscosity as a function of temperature. Almost at the same time, Arrhenius assumed (1889) similar equations for the temperature dependence of reaction rates. Now, exponential functions are the most important and widespread functions in physics, chemistry and biology. Similarly, in physics, exponential functions describe the decay of radioactive nuclei [1], the emission of light by atoms [2], and electrical conductivity in various semiconductors [3–5] and even in superconductors [6]. In biology, exponential functions describe the growth of bacterial, viral or animal populations [7,8]. However, attempts to find any non-exponential dependence of the rates of chemical reactions on temperature continue to this day. For example, to improve the description of the temperature dependence of the rate constants for functions that differ from Arrhenius’ theory, work based on empirical two-parameter functions with two ”non-Arrhenian” temperatures was performed [9–14]. However, these models and aspects are not the focus of this review. Empirical models of processes usually work for a limited range of temperatures, and are expressed in a universal form or the universal Arrhenius equation [15]: ϕ(T)= A 0 · e (− E A k B T ) (1) where ϕ(T) is, as a rule, the rate of a thermally activated process; k B is the Boltzmann constant; E A is the sensitivity of the process to the temperature or the activation energy (in the case of reaction rates). The physical meaning of all the above-named exponential Thermo 2021, 1, 45–60. https://doi.org/10.3390/thermo1010004 https://www.mdpi.com/journal/thermo