The missing link in the kinetic theory of chemical reactions and epidemics

Vanel, L.

In thermodynamics, affinity is the driving force of chemical reactions. At equilibrium, affinity is zero, and the reaction quotient equals the constant of equilibrium. Thermodynamics predicts the timescale of chemical reactions but not rate laws that are purely phenomenological relations. Here, we derive an affinity relaxation theory (ART) that predicts chemical rate laws. Strikingly, the simplest chemical reaction in the ART model has a close resemblance with epidemic models instead of the mass-action rate law, revealing that epidemic models are actually more accurate chemical rate laws than the mass-action law. However, epidemic models appear in turn as an approximation of the ART model, where conceptual incoherencies of epidemic models are exposed and resolved. Furthermore, the mathematical Gompertz solution of the model links chemical rate laws with empirical biological and cancer growth laws. The ART model provides an entirely new framework to describe dynamic phenomena in chemical reactions, epidemics and biology.