  In statistical physics, the conservation of particle number results in the
equalization of the chemical potential throughout a system at equilibrium. In
contrast, the homogeneity of utility in socio-economic models is usually
thought to rely on the competition between individuals, leading to Nash
equilibrium. We show that both views can be reconciled by introducing a notion
of chemical potential in a wide class of socio-economic models, and by relating
it in a direct way to the equilibrium value of the utility. This approach also
allows the dependence of utility across the system to be determined when agents
take decisions in a probabilistic way. Numerical simulations of a urban
economic model also suggest that our result is valid beyond the initially
considered class of solvable models.
