"Glassy" Relaxation in Catalytic Reaction Networks

TL;DR

This paper investigates slow, glass-like relaxation behaviors in reversible catalytic reaction networks, highlighting the roles of eigenvalue distributions and kinetic constraints in these dynamics.

Contribution

It introduces a novel analysis of glassy relaxation phenomena in catalytic networks, linking eigenvalue spectra and kinetic constraints to observed slow dynamics.

Findings

Logarithmic time dependence of correlation functions.

Emergence of relaxation plateaus due to kinetic constraints.

Kinetic constraints, not metastability, cause glassy behavior.

Abstract

Relaxation dynamics in reversible catalytic reaction networks is studied, revealing two salient behaviors that are reminiscent of glassy behavior: slow relaxation with log(time) dependence of the correlation function, and emergence of a few plateaus in the relaxation. The former is explained by the eigenvalue distribution of a Jacobian matrix around the equilibrium state that follows the distribution of kinetic coefficients of reactions. The latter is associated with kinetic constraints, rather than metastable states, and is due to the deficiency of catalysts for chemicals in excess and negative correlation between the two chemical species. Examples are given, and generality is discussed.