Thermodynamic Approach to the Problem of Economic Equilibrium

Abstract

Economic theory represents the unusual case when the ontological assumptions underlying mathematical models are somewhat mathematical models themselves, or more precisely, mathematical metaphors. A basic mathematical metaphor for the classical model of the market is mechanical equilibrium. The basic idea of such a model is that small deviations of the system from a point of equilibrium result in occurrence of “forces”, which cause the system to return to the state of equilibrium. In some, very important sense, “the invisible hand” of the market in this model is equivalent to a mechanical force. The economy is considered as a dynamic system. Time stands as a key notion, and the mathematical structure of the economic models is represented by ordinary differential equations. Equilibrium is considered in the mechanical models as a state at which forces applied to the system counterbalance each other, and the potential energy achieves a minimum.¹ Consequently, for applications of the mechanical metaphor of equilibrium to economic theory, some analogues of the mechanical notions are needed. But this conceptualization is not completely harmless. It implies that, upon deviation from the state of equilibrium, the system, acting by itself, will return to this very state. It is well known that there are also some other approaches in physics to the conceptualization of the intuitive notion of equilibrium. In this context, thermodynamic equilibrium should be mentioned first of all. According to this concept, the system approaches a state of equilibrium not because it is being affected by “forces”, but because this is the most probable state of the system, consisting of parts, each of which is characterized by its independent dynamics.