What is the Obidi Bridge Equation (OBE) of the Theory of Entropicity (ToE)?

The Obidi Bridge Equation (OBE) is a conceptual framework within the Theory of Entropicity (ToE), a, emerging, and largely independent theoretical framework developed by John Onimisi Obidi (2025–2026). It is a central part of a new, highly specialized approach to unified physics. 

Note: Based on the search results, this refers to a very recent (late 2025) theoretical physics paper by independent researcher John Onimisi Obidi. 

Core Concept and Definition
The Theory of Entropicity (ToE) posits that entropy is not merely a statistical measure of disorder but a fundamental physical field that generates spacetime, motion, gravity, and time. 

• The "Bridge": The Obidi Bridge Equation serves to connect different physical realms within this framework, specifically bridging the gap between local entropic field dynamics and global spectral operator theory.
• The Equation(s): The "bridge" is established by connecting two main formulations:
  1. Local Obidi Action: Describes the differential, local dynamics of the entropy field (leading to the "Master Entropic Equation").
  2. Spectral Obidi Action: Expresses the same physics globally via operator traces.
• Function: It allows researchers to move between local field equations (similar to general relativity) and global spectral consistency (similar to quantum field theory). 

Key Implications 

• Unified Theory: The equation connects thermodynamic, quantum mechanical, and gravitational constants (ℏc=kBTsℓs).
• Gravity as Entropy: It supports the idea that gravity is not a primary force but a result of entropic gradients in spacetime.
• Irreversibility: It introduces irreversibility directly into quantum dynamics.
• Structure: It establishes that matter is "localized entropic condensation" and motion is the "redistribution of entropic gradients". 

Origin
The equation is developed in papers by John Onimisi Obidi (e.g., "On the Theory of Entropicity (ToE) and Ginestra Bianconi's Gravity from Entropy," 2025). It is being analyzed as a competitor or extension to other entropic-gravity theories and is designed to resolve issues like dark energy and quantum-gravitational correspondence. 

Appendix: Extra Matter

The Obidi Bridge Equation (OBE), also referred to as part of the Obidi Action or the Spectral Obidi Action within the Theory of Entropicity (ToE), is a theoretical physics construct developed by John Onimisi Obidi. It represents a mathematical bridge connecting local entropic field dynamics with global, operator-based spectral geometry. 

Here is a breakdown of the Obidi Bridge Equation and its context within the Theory of Entropicity: 

• Definition: The OBE is the duality link between the Local Obidi Action (which describes the differential dynamics of the entropy field) and the Spectral Obidi Action (which describes the system globally through operator traces).
• Purpose: It bridges the gap between local field equations (classical/general relativity) and quantum spectral consistency, specifically by connecting equilibrium geometry to its matter-deformed counterpart through a modular operator.
• Entropic Context: In the Theory of Entropicity, entropy is treated as a fundamental, physical field
  

  $S\left(x\right)$
  rather than a statistical, disorder-based, or derivative concept. The OBE facilitates the interpretation of gravity, matter, and quantum correlations as emergent properties of this entropic field's gradients.
• Key Distinctions: The OBE differs from prior entropy-based theories by integrating bosonic and fermionic dynamics within a single entropic-spectral framework and resolving challenges related to quantum gravity (e.g., dark matter and the cosmological constant).
• Relationship to Other Theories: The framework extends the work of Ginestra Bianconi on "Gravity from Entropy" by identifying her auxiliary fields as natural spectral consequences of the entropic field, placing her results as a specific, quasi-equilibrium case within the broader, more fundamental Obidi Action. 

The Theory of Entropicity aims to unify quantum mechanics, thermodynamics, and general relativity by redefining the fundamental substrate of the universe. 

References

1)

 https://share.google/aimode/6w43vUjHMx7K3cDah

2)

 https://share.google/aimode/WoZzJJkGHv4x4V70u