How does a system’s relaxation time relate to its reaction rates?

In the study of chemical kinetics, a system’s relaxation time ($\tau$) is fundamentally linked to its reaction rates and the underlying reaction mechanism.12

When a system at chemical equilibrium is subjected to a rapid external disturbance—such as a sudden change in temperature or pressure—it does not return to equilibrium instantaneously. Instead, the concentrations of reactants and products adjust at a finite rate until a new balance is established. The relaxation time represents the time constant for this re-equilibration process.321

The relationship functions as follows:
* Determining Rates: By measuring the relaxation time, scientists can derive the specific rates at which reactants combine and dissociate. Because the rate of re-equilibration is limited by the concentrations and reactivities of the species involved, the relaxation time provides a direct window into these kinetic properties.34
* Mechanism Insight: If the reaction mechanism is known, the relaxation time can be calculated from the reactivities of the reactants. Conversely, by observing how the relaxation time changes with reactant concentrations, researchers can deduce the specific mechanism of the reaction.1
* Complex Systems: In systems where multiple reactions are coupled, a spectrum of relaxation times may be observed, representing the normal modes of the system.1

This relaxation method, pioneered by Manfred Eigen, allows for the study of extremely fast reactions that are otherwise difficult to measure using traditional mechanical mixing techniques.45