A unified theory of emergent equilibrium phenomena in active and passive matter

Abstract

Recent attempts towards a theory of active matter utilize concepts and methods from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, such approaches typically do not seem to recognize the critical feature of some kinds of active matter (particularly the biological ones), namely, the role of purpose, and the naturally attendant concept of the pursuit of maximum utility, which we believe is the crucial difference between active and passive matter. Here we introduce a novel game-theoretic framework, statistical teleodynamics, that accounts for this feature explicitly and show how it can be integrated with conventional statistical mechanics to develop a unified theory of arbitrage equilibrium in active and passive matter. We propose a spectrum of self-actualizing capabilities, going from none to completely strategic decision-making, and envision the various examples of active matter systems occupying someplace in this spectrum. We 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 about the emergence of income distributions and their fairness in an ideal free-market society. As examples of agents in between these limits, we show how our theory predicts the behavior of active Brownian particles, the emergence of ant craters, and phase equilibria in social segregation dynamics. We suggest that our theory offers a novel systems theoretic perspective of emergent phenomena that could serve as the starting point for a more comprehensive theory of design, control, and optimization through self-organization.