Effective Free Energy for Individual Dynamics

TL;DR

This paper introduces a generalized free energy framework combining statistical mechanics and game theory to analyze individual dynamics in socio-economic models, enabling analytical solutions for complex systems.

Contribution

It presents a novel rigorous generalization of free energy that incorporates individual choices, bridging physics and economics for better analytical modeling.

Findings

Derived solutions for congestion models

Analyzed residential segregation dynamics

Provided a new analytical framework for socio-economic systems

Abstract

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.