Entropy and equilibrium state of free market models

• Published in: arXiv.org
• Main Authors: Iglesias, J R, R M C de Almeida
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 29.08.2011
• Subjects: Economic conditions; Economic models; Entropy; Equilibrium; Exchanging; Mathematical models; Physics - Physics and Society; Quantitative Finance - General Finance
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1108.5725

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.