q-Exponential Structure of Arbitrary-Order Reaction Kinetics

Abstract

The rate equation for an arbitrary mth order growth or decay reaction can be expressed in terms of the q-exponential function, with q equal to m. The analysis suggests that a wide variety of reaction rate (kinetic) processes and models, in chemistry, biology/ecology, unit operations and contaminant transport, are amenable to analysis by Tsallis' non-extensive statistical mechanics. A number of q-analogues of common kinetic mathematical models are proposed, and illustrated by several examples.