On the mathematical theory of living systems, I: Complexity analysis and representation

This paper is the first one of a sequel devoted to the challenging goal of developing a mathematical theory for living systems. We consider systems constituted of a number of living entities, called active particles, which have the ability to express specific strategies and interact with other entities. The author proposes a personal path, starting from the identification of a number of common features of living systems that can be viewed as sources of complexity, focusing specifically on the representation of systems based also on a strategy to reduce their complexity. The overall system is decomposed into functional subsystems whose representation is delivered by a probability distribution over the microscopic state of the active particles belonging to such system. Looking ahead, this paper indicates some guidelines to derive mathematical structures, where interactions involving active particles are nonlinearly additive.