Entropy for a class of micro-economic models

2025/10/02 by Robert S. MacKay, MacKay, Robert S
Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2510.01737

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Convergence to equilibrium for a class of exchange economies
• Thermal Macroeconomics: An axiomatic theory of aggregate economic phenomena
• Tests of thermal macroeconomic theory on simulated micro-economies
• The Mathematical Structure of the Second Law of Thermodynamics

Related

• Statistical thermodynamics of economic systems
• Nonequilibrium Entropy in an Extended State Space
• Occam's Razor Cuts Away the Maximum Entropy Principle
• On microscopic entropy production, heat and fluctuation theorem
• Utility Function from Maximum Entropy Principle