What is life? Active particles tools towards behavioral dynamics in social-biology and economics

This review paper is devoted to study the conceptual difficulties that mathematics meets when attempting to describe the com-plexity of living matter focusing on the challenging perspective of developing a mathematical theory for living systems including mutations and selection. The quest starts with the identification of a number of common complexity features of living systems. Then, mathematical structures are derived to include these features, while mathematical models are derived by inserting in the structures models of individual based interactions. Three applications are examined by active particles methods, i.e., models of SARS2-CoV-2 pandemics, models of idiosyncratic learning in open markets and of the dynamics of prices accounting for human behaviors. A critical study, which pervades the whole paper, shows that also economics can be viewed as a behavioral science thus accounting for specific aspects typical of living systems.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This review paper examines the conceptual difficulties that mathematics faces in describing the complexity of living matter, with a focus on developing a mathematical theory for living systems that includes mutations and selection. The paper identifies common complexity features of living systems and derives mathematical structures and models to incorporate these features. The applications discussed include models of SARS2-CoV-2 pandemics, idiosyncratic learning in open markets, and the dynamics of prices considering human behaviors. Throughout the paper, there is a critical analysis that demonstrates economics can be seen as a behavioral science and accounts for specific aspects of living systems.