Turbulence in the Geometry of Power

This paper develops a statistical mechanics approach for studying turbulence in political dynamics based on action functionals, entropy, and stochastic evolution. Political trajectories are modeled as paths in a high-dimensional state space, weighted by a generalized action functional that incorporates structural constraints and exogenous pressures. This formulation induces a path-integral representation of political evolution, from which entropy and a state-dependent free-action functional are derived. The resulting macroscopic dynamics are governed by a Langevin equation, in which drift is determined by the gradient of the free action and diffusion reflects turbulence in the system. The associated Fokker–Planck equation describes the time evolution of probability densities over political states, providing a distributional characterization of regime stability and transition likelihoods. Monte Carlo simulation is used to approximate the stochastic dynamics and generate empirical distributions of political states of regime behavior under varying conditions of temperature and pressure that give rise to turbulence. Applied to six East African countries (Ethiopia, Kenya, Rwanda, South Sudan, Tanzania and Uganda) the study’s finding provide an effective framework for interpretation of political stability and instability. In summary, the study offers a cohesive quantitative approach to understanding stability, volatility, and structural transitions in political establishments.