The rate coefficients of unimolecular reactions in the systems with power-law distributions

TL;DR

This paper generalizes unimolecular reaction rate coefficients to systems with power-law distributions using nonextensive statistics, deriving formulas for high and low pressure limits and validating with experimental data.

Contribution

It introduces a new formulation of rate coefficients based on nonextensive statistics, extending traditional models to power-law distributed systems.

Findings

Rate coefficients depend strongly on the nu-parameter, differing from classical models.

Derived formulas agree with experimental data for specific reactions.

Power-law rate coefficients can match experimental results with nu-parameters near one.

Abstract

The rate coefficient formulae of unimolecular reactions are generalized to the systems with the power-law distributions based on nonextensive statistics, and the power-law rate coefficients are derived in the high and low pressure limits, respectively. The numerical analyses are made of the rate coefficients as functions of the nu-parameter, the threshold energy, the temperature and the number of degrees of freedom. We show that the new rate coefficients depend strongly on the nu-parameter different from one (thus from a Boltzmann-Gibbs distribution). Two unimolecular reactions are taken as application examples to calculate their power-law rate coefficients, which obtained with the nu-parameters slightly different from one can be exactly in agreement with all the experimental studies on these two reactions in the given temperature ranges.