The Generalized Reaction Rate Theories in the Systems with Power-Law Distributions

Abstract

The calculations of reaction rate are important in studying the different processes in physics, chemistry, biology, engineering etc. There exist many theories of reaction rate, such as transition state theory, collision theory, and unimolecular reaction theory. One key assumption in these theories is that thermodynamic equilibrium prevails throughout the entire system studied for all degrees of freedom. According to the Boltzmann-Gibbs statistical mechanics, a Maxwell-Boltzmann distribution whose form is exponential law holds in the whole time. This exponential law form of reaction rate is usually called Arrhenius behavior in chemistry. However, plenty of experimental results show non-Arrhenius behavior, such as power-law behavior. Besides, in reacting systems, the processes of evolution from one meta-stable state to another neighboring metastable state happen all the time, therefore the equilibrium assumption would be quite far-fetched. In these cases, current theories are no longer valid, and they can not even serve as a conceptual guide for understanding the critical factors that determine rates. Therefore, providing corresponding theoretical description for non-Arrhenius behavior or power-law behavior becomes urgent. In this general paper, generalized reaction rate theories with power-law distributions in the framework of nonextensive statistical mechanics were discussed based on experimental and observing facts.

The collision theory of unimolecular reactions: A second possibility to Lindemann’s proposal

“…Determination or modelling of systems with varying rates of chemical interactions have remain an important subject of inquiry in various disciplines of endeavors such as chemistry, physics, biology, and engineering (Yin 2015;Mortiner 2008;Roselar 1975). Various modifications and treatments of models help us improve on the existing theories of unimolecular reactions (Turanyi and Tomlin 2014).…”