The Geometry of Power

This paper develops the Geometry of Power , a path-integral framework for analyzing political regime dynamics under uncertainty. Extending the Calculus of Power , which models regime behavior through real options and optimal control, the Geometry of Power replaces single optimal trajectories with ensembles of admissible political histories weighted by an action functional. This formulation enables the introduction of path entropy, state entropy, and free action as structural descriptors of political accessibility and robustness. Using Monte Carlo simulations calibrated with political, economic, and conflict indicators, the framework is applied to six East African countries—Ethiopia, Kenya, Rwanda, South Sudan, Tanzania and Uganda—to evaluate the relative accessibility of democratic, authoritarian, military, and collapsed regime endpoints. The results show that regime persistence and transition are governed not solely by cost minimization, but by an entropy-regularized geometry that conditions rational political behavior under uncertainty. Authoritarian configurations emerge as structurally robust under prevailing regional constraints, while democratic transitions occupy narrow and fragile corridors. These findings offer a non-deterministic, value-neutral explanation of regime dynamics, emphasizing structural conditioning rather than inevitability or normative prescription.