Entropy and equilibrium state of free market models

TL;DR

This paper explores how certain economic exchange models lead to minimum entropy states with wealth concentration, contrasting with physical systems that tend toward maximum entropy and equilibrium.

Contribution

It introduces an analytical model to study economic exchanges that minimize entropy, revealing conditions for wealth concentration and mechanisms for restoring wealth distribution.

Findings

Certain exchange rules lead to wealth condensation.

Conditions for minimum entropy states are identified.

Mechanisms to restore wealth equality are discussed.

Abstract

Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. In physical systems, the energy exchange among molecules leads to a state of equipartition of the energy and to an equilibrium situation where the entropy is a maximum. On the other hand, in the majority of exchange models, the system converges to a very unequal condensed state, where one or a few agents concentrate all the wealth of the society while the wide majority of agents shares zero or almost zero fraction of the wealth. So, in those economic systems a minimum entropy state is attained. We propose here an analytical model where we investigate the effects of a particular class of economic exchanges that minimize the entropy. By solving the model we discuss the conditions that can drive the system to a state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of wealth.