Institutional Phase Transitions and Power Concentration. A Statistical Mechanics Model of Economic Networks.

Institutional instability and the concentration of economic power are often analyzed through historical or qualitative frameworks. In this work we propose a quantitative model that interprets institutional collapse as a phase transition in a complex socio-economic system. We introduce an order parameter $D = MH$ which combines the capital share of income $M$ with a structural concentration index $H$. The micro-level dynamics of power shares are modeled through replicator dynamics on an influence network, while the macroscopic behavior of the system is described by an effective Landau free energy potential. Within this framework we show that the institutional system exhibits a continuous phase transition between dispersed and concentrated power regimes. The stochastic dynamics of the order parameter are derived using a Langevin formulation, leading to a Fokker–Planck equation whose stationary solution corresponds to a Boltzmann-type distribution over institutional states. The model predicts the emergence of critical thresholds, hysteresis effects, universal scaling laws, and early warning signals such as variance divergence and critical slowing down. Numerical experiments and empirical illustrations highlight the bifurcation structure and the stochastic evolution of the order parameter across different regimes. The results suggest that the interaction between macroeconomic resource distribution and network concentration may generate universal patterns of institutional instability analogous to critical phenomena in statistical physics, situating the framework within the mean-field universality class.