  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.
