From classical to active particles: mathematical tools for social dynamics and behavioural economics.

This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution. The main objective is to study the interactions of large systems of living entities mathematically. More specifically, the study relates to the complex features of living systems and the mathemat ical tools inspired by statistical physics. The focus is on the mathemati cal description of these interactions and their role in deriving differential systems that describe the aforementioned dynamics. The paper demon strates that studying these interactions naturally yields new mathematical insights into systems in the natural sciences and behavioral economics.