Eur. Phys. J. B (2012) 85: 85
https://doi.org/10.1140/epjb/e2012-21036-1

Regular Article

Entropy and equilibrium state of free market models

¹ Instituto de Física, UFRGS, and Instituto Nacional de Ciência e Tecnologia de Sistemas Complexos, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazil
² Programa de Pós-Graduação em Economia Aplicada, UFRGS, Av. João Pessoa 52, 90040-000 Porto Alegre, RS, Brazil

^a e-mail: roberto.iglesias@ufrgs.br

Received: 15 December 2011
Received in final form: 11 January 2012
Published online: 5 March 2012

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 a large class 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.