The physics of active matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Recent theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these don’t seem to recognize explicitly their critical feature, namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. In this talk, I will present a novel game-theoretic framework, statistical teleodynamics, that accounts for this feature explicitly and shows how it can be integrated with conventional statistical mechanics to develop a unified theory of arbitrage equilibrium in active and passive matter.

The theory proposes a spectrum of self-actualizing capabilities, going from none to completely strategic decision-making, and envisions the various examples of active matter systems occupying someplace in this spectrum. I will show how statistical teleodynamics reduces to familiar results in statistical mechanics in the limit of zero self-actualization. At the other extreme, in an economic setting, it provides novel insights into the emergence of income distributions and their fairness in an ideal free-market society. As examples of agents in between these limits, I will discuss how the theory predicts pattern formation in mussel beds, the emergence of ant craters, and the flocking of birds.