Core Foundations, Mathematical Pillars and Emergent Phenomena of the Theory of Entropicity (ToE)

The Theory of Entropicity (ToE), formulated by John Onimisi Obidi in 2025, is a radical framework in theoretical physics that elevates entropy from a secondary statistical measure to the fundamental, "ontic" field of reality. It proposes that space, time, gravity, and quantum mechanics are not primary entities but emergent manifestations of this dynamic entropic field. 

Core Foundations 

• Entropy as a Fundamental Field: ToE departs from the traditional view of entropy as disorder. Instead, it posits an autonomous ontological scalar field
  

  $S(x,t)$
  that permeates existence and drives all physical evolution.
• The No-Rush Theorem: This central principle asserts that "Nature cannot be rushed." No physical interaction or state change can occur instantaneously; every event requires a finite, non-zero duration for the entropic field to rearrange itself.
• Speed of Light as an Entropic Rate: The universal constant
  

  $c$
  is reinterpreted as the maximum rate of entropic reconfiguration. It is not an arbitrary speed limit but a property of the entropic medium itself—the "processing speed" of the universe.
• Information-Geometry Bridge: Using tools from information geometry (e.g., Fisher-Rao and Fubini-Study metrics), the theory mathematically links the flow of information to physical spacetime curvature. Curvature is seen as the "geometric shadow" of entropy flow. 

Mathematical Pillars 

• The Obidi Action: A universal variational principle that determines the dynamics of the entropic field, analogous to the Einstein-Hilbert action in General Relativity.
• Master Entropic Equation (MEE): Derived from the Obidi Action, the MEE governs how entropy gradients evolve and couple to matter and geometry.
• Temperature of Information: ToE introduces an intrinsic temperature for information and geometry, defined by the rate of informational change rather than molecular motion. With this insight from the Theory of Entropicity (ToE), Obidi derived the famous Casimir Effect of Quantum Field Theory (QFT). 

Emergent Phenomena 

• Gravity: Rather than a fundamental force, gravity is an emergent effect caused by mass creating entropic gradients that systems naturally move to maximize.
• Relativity: Relativistic effects like time dilation and length contraction are derived as entropic inevitabilities resulting from how the field redistributes a finite "entropic budget" between motion and internal processes.
• Time: Time is reinterpreted as the sequential update of the field's configuration as entropy flows irreversibly. 

Would you like to explore the mathematical derivation of a specific relativistic effect—such as time dilation—within this entropic framework?