  In recent years, significant progress in generative AI has highlighted the
important role of physics-inspired models that utilize advanced mathematical
concepts based on fundamental physics principles to enhance artificial
intelligence capabilities. Among these models, those based on diffusion
equations have greatly improved image quality. This study aims to explore the
potential uses of Maxwell-Boltzmann equation, which forms the basis of the
kinetic theory of gases, and the Michaelis-Menten model in Marketing Mix
Modelling (MMM) applications. We propose incorporating these equations into
Hierarchical Bayesian models to analyse consumer behaviour in the context of
advertising. These equation sets excel in accurately describing the random
dynamics in complex systems like social interactions and consumer-advertising
interactions.
