Reaction Rates in Quasiequilibrium States

TL;DR

This paper explores how non-Maxwellian, quasiequilibrium distributions modeled by superstatistics affect reaction rates, especially in fusion and plasma processes, revealing conditions where they outperform traditional Maxwellian assumptions.

Contribution

It introduces a framework for analyzing reaction rates in quasiequilibrium systems using superstatistics, extending understanding of nonequilibrium effects on reaction kinetics.

Findings

Superstatistics classes significantly influence reaction rates.

Quasiequilibrium distributions can enhance fusion reactivities.

Nonequilibrium effects alter ionization and recombination rates.

Abstract

Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on processes and quantities that strongly depend on the energy distribution, such as reaction rates. In this paper, we investigate reaction rates in the general context of quasiequilibrium systems, which exhibit only local equilibrium. The hierarchical structure of these systems allows their statistical properties to be represented as a superposition of statistics, i.e., superstatistics. Focusing on the three universality classes of superstatistics--$\chi^2$, inverse-$\chi^2$, and log-normal--we examine how these nonequilibrium distributions influence reaction rates. We analyze, both analytically and numerically, reaction rates for processes involving tunneling phenomena, such as fusion, and identify conditions under which quasiequilibrium distributions outperform Maxwellian distributions in enhancing fusion reactivities. To provide a more detailed quantitative analysis, we further employ semi-empirical cross sections to evaluate the effect of these nonequilibrium distributions on ionization and recombination rates in a plasma.