Measuring disorder in irreversible decay processes

TL;DR

This paper introduces a method to quantify disorder in irreversible decay processes by relating rate coefficients to Fisher information, enabling the measurement of fluctuations and disorder in kinetic systems.

Contribution

It establishes a novel relationship between rate coefficients and Fisher information, defining kinetic statistical measures to quantify disorder in decay kinetics.

Findings

Kinetic measures of disorder are derived from Fisher information.

The difference between statistical-length squared and divergence quantifies disorder.

Disorder measure is zero for unique, non-fluctuating rate coefficients.

Abstract

Rate coefficients can fluctuate in statically and dynamically disordered kinetics. Here we relate the rate coefficient for an irreversibly decaying population to the Fisher information. From this relationship we define kinetic versions of statistical-length squared and divergence that measure cumulative fluctuations in the rate coefficient. We show the difference between these kinetic quantities measures the amount of disorder, and is zero when the rate coefficient is temporally and spatially unique.