(650j) Statistical Teleodynamics: A Novel Framework for Unifying the Physics of Active and Passive Matter

Statistical thermodynamics is the conceptual framework for predicting certain key aspects (e.g., equilibrium energy distribution) of the macroscopic behavior of a thermodynamic system given certain properties of the millions of individual “passive” entities (e.g., molecules) that make up the system. As “prisoners” of Newton’s laws and conservation principles, molecules do not have control over their “fates” or their dynamical trajectories; their dynamical evolution is the result of thermal agitation resulting from incessant intermolecular collisions. Nor do the molecules have “free will” that would make them desire one path over another.

But what if the entities possessed free will and had the ability to decide what to do next? What would be a statistical mechanics-like framework for predicting the macroscopic behavior of a large collection of such rational, intelligent, goal-driven agents?

Recently, Venkatasubramanian [2017a, 2017b] proposed such a conceptual framework, called statistical teleodynamics, and showed its ability to predict income distributions in capitalist societies. This new framework reveals a hitherto unknown deep connection between the statistical mechanics of “passive” agents and the game theory of “rational” agents. This important connection arises through two fundamental concepts, entropy and chemical potential. It turns out that entropy is the same as game theoretic potential under certain conditions, and the chemical potential is equivalent to utility of the agents. Thus, game theoretic economic equilibrium, which is Nash equilibrium, is reached when all the rational agents enjoy the same utility. This is equivalent to the statistical or chemical equilibrium that is reached when the chemical potentials are equal for “passive” matter.

In this talk, we show how this theory predicts and explains certain phenomena in active matter physics. It turns out that the physics of active matter fits in between the physics of passive matter and the “physics” (i.e., economics) of rational agents. Thus, far-from-equilibrium phenomena of active matter systems could be explained with a statistical mechanics-like equilibrium formulation of such systems. Our framework adopts a utilitarian approach – one where an individual agent tries to maximize its utility and self-organization is achieved as a result of collective evolution of interacting agents. We show that such an approach naturally introduces the concept of entropy maximization, and the different constraints imposed on the system (and agents) result in different distributions characterizing the self-organizing patterns. Furthermore, the framework accommodates the presence of multiple populations of agents – compatible or incompatible – with the concept of cross-entropy that generalizes to systems with any number of competing populations. While the individual agent in the system attempts to maximize its utility, equilibrium of the system as a whole is shown to be achieved through maximization of entropy and cross-entropy. The framework predicts the behavior of passive (gas molecules, oil-water mixture) as well as active matter (ant and termite mounds).

References:

Venkatasubramanian, V., How Much Inequality Is Fair?: Mathematical Principles of a Moral, Optimal, and Stable Capitalist Society, Columbia University Press, 2017.

Venkatasubramanian, V., “Statistical teleodynamics: toward a theory of emergence”,

Langmuir 33 (42), 11703-11718, 2017.