qq-Exponential structure of arbitrary-order reaction kinetics

The rate equation for an arbitrary mmth-order growth or decay reaction can be expressed in terms of the qq-exponential function expqf=[1+(1-q)f]1/(1-q)expqf=[1+(1-q)f]1/(1-q), with qq equal to mm. 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 qq-analogues of common kinetic mathematical models are proposed, and illustrated by several examples.