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The Geometry of Power: Path Integrals in the Dynamics of Political Regimes

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  • Edward, Caesar

Abstract

This paper, "The Geometry of Power," presents a path-integral framework for analyzing the dynamics of political regimes under uncertainty. Whereas the earlier work, The Calculus of Power, focused on optimal paths, the present approach replaces single optimal paths with ensembles of permissible political histories, each weighted by an action functional. In this paper, we also introduce the concepts of path entropy, state entropy, and free action to describe the structures of political accessibility and strength. We then used Monte Carlo simulations, calibrated with political, economic, and conflict indicators, to test the validity of the framework on six East African countries: Ethiopia, Kenya, Rwanda, South Sudan, Tanzania, and Uganda. The aim of the analysis is to evaluate the relative accessibility of democratic, authoritarian, military, and collapsed regime endpoints. The results show that the stability of regimes and shifts is governed not only by minimizing costs but also by the “entropy of the geometry” that shapes rational political behavior under uncertainty. Authoritarian regimes are found to be structurally strong under prevailing regional constraints. However, democratic transitions are restricted to narrow and fragile pathways.

Suggested Citation

  • Edward, Caesar, 2026. "The Geometry of Power: Path Integrals in the Dynamics of Political Regimes," SocArXiv t9pur_v1, Center for Open Science.
    • Handle: RePEc:osf:socarx:t9pur_v1
    DOI: 10.31219/osf.io/t9pur_v1
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    References listed on IDEAS

    as
    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, December.
    2. Edward, Caesar, 2025. "Calculus of Power Real Options in the Dynamics of Political Regimes," SocArXiv fyhtp_v2, Center for Open Science.
    3. Acemoglu,Daron & Robinson,James A., 2009. "Economic Origins of Dictatorship and Democracy," Cambridge Books, Cambridge University Press, number 9780521671422, Enero-Abr.
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