Entropy for a class of micro-economic models

TL;DR

The paper formalizes an entropy framework for a broad class of micro-economic exchange economies in the thermodynamic limit, showing that an entropy function exists under Lieb–Yngvason axioms and that the economic entropy equals $S = \log Z$ (up to additive constants). It proves that four trader interaction modes (including financial and trading contact) can only increase or preserve the total extensive entropy, and that money can drive entropy upward through increased $Z$, thereby connecting micro-agent dynamics to a macro entropic description. The main contributions are the rigorous identification of $\log Z$ as the entropy, the verification of the axioms in this economic setting, and the demonstration of the canonical ensemble's relevance for practical computations. The results provide a formal thermodynamic and informational perspective on gains from trade, money flows, and price formation in large-scale agent-based economies, with potential implications for inflation and monetary value concepts.

Abstract

Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not decrease. In this paper, a large class of agent-based models is proved to satisfy the axioms in the thermodynamic limit, and the entropy is shown to be the logarithm of the partition function for their stationary distributions.