Statistical Entropy in General Equilibrium Theory

This essay seeks to develop an integrated account of the workings of statistical mechanics and thermodynamics as a theory of economic equilibrium. It begins with a probabilistic description of general systems (made out of numerous elements), based on the practice of statistical physics and the work of E. T. Jaynes, and a self-contained overview of the arguments that lead to the concept of statistical entropy as a measure of uncertainty or disorder and the maximum statistical entropy principle . This provides the conceptual setting for developing a statistical mechanical model of general equilibrium in pure exchange economies, inspired by the statistical theory of markets of Duncan K. Foley. Emphasis is placed in the derivation of the properties of the entropy function of an economy—the maximized statistical entropy as a function of the amounts of resources in that economy. We then show that the statistical equilibrium theory of pure exchange economies gives rise to a phenomenological or ‘macro’ theory of resource allocation in the image of classical thermodynamics (and the generalized thermodynamics of L. I. Rozonoer). We thus establish the fundamental principle of the phenomenological theory—the maximum entropy principle—and illustrate its use for the study of isolated and small open economies.statistical entropy, thermodynamics, general equilibrium, physics