Vuli-Ndlela Integral

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The Vuli-Ndlela Integral of the Theory of Entropicity(ToE)

The Vuli-Ndlela Integral of the Theory of Entropicity(ToE) is the Feynman Path Integral formulation of Quantum Theory with entropy weighted parameters and functions. In the Feynman formulation, the integral is a sum over all possible paths and histories of interactions; that is, all paths are equally feasible point sets on the trajectory of motion of any given particle or event. However, in the Vuli-Ndlela Integral approach, all paths are not placed on equal footing; here, the sum is not over all possible paths but only on paths allowed by entropic constraints: entropy allows some paths, and disallows other paths. So, in the Theory of Entropicity(ToE)[1] — first formulated and developed by John Onimisi Obidi[2][3] — only those paths realized and permitted by entropy contribute to the final equations of motion and interaction of any given particle or event.

This is the Feynman Path Integral:


This is the Vuli-Ndlela Integral:




  1. Obidi, John Onimisi. A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty. Cambridge University.(2025-06-30). https://doi.org/10.33774/coe-2025-hmk6n
  2. Obidi, John Onimisi. Einstein and Bohr Finally Reconciled on Quantum Theory: The Theory of Entropicity (ToE) as the Unifying Resolution to the Problem of Quantum Measurement and Wave Function Collapse. Cambridge University. (14 April 2025). https://doi.org/10.33774/coe-2025-vrfrx
  3. Obidi, John Onimisi (2025). Master Equation of the Theory of Entropicity (ToE). Encyclopedia. https://encyclopedia.pub/entry/58596