Physics:The Obidi Action in the Theory of Entropicity(ToE)

Introduction

The Obidi Action is a central construct within the Theory of Entropicity(ToE), introduced by John Onimisi Obidi. It represents a novel variational principle in which the fundamental quantity is entropy rather than curvature or fields in the traditional sense. The Obidi Action is “pure-entropic” in character: it posits that entropy [math]\displaystyle{ S(x) }[/math] itself is the universal scalar field from which geometry, dynamics, information, and even consciousness emerge.

In analogy with the Einstein–Hilbert action of General Relativity, the Obidi Action generates the Master Entropic Equation (MEE) through a variational process. It encodes the dynamics of entropy flows, irreversibility, and informational geometry, thereby offering a unifying principle that connects physics, information theory, and consciousness.

Entropic Foundation

Unlike conventional field theories that begin with matter fields or spacetime curvature, the Obidi Action treats entropy as the primitive field:

• Entropy is modeled as a local, dynamic, scalar field [math]\displaystyle{ S(x) }[/math].
• The arrow of time and irreversibility are built into the action at a fundamental level.
• Geometry and physical interactions are emergent consequences of entropic gradients and flows.

This formulation elevates entropy from a statistical descriptor to the governing principle of physical law.

Composite Functionals

The Obidi Action integrates multiple structures into entropy dynamics by defining them as functionals of the entropy field:

• Metric Tensor [math]\displaystyle{ g_{\mu\nu}(S) }[/math] emerges as a functional of entropy.
• Connection [math]\displaystyle{ \Gamma^\mu_{\nu\rho}(S) }[/math] arises from entropic flows and defines entropic geodesics.
• Information Geometry is encoded in entropy, binding the probabilistic structure of states with the physical structure of the universe.

Thus, the Obidi Action provides a composite framework unifying spacetime geometry, information theory, and thermodynamics.

Variational Principle

The action functional (of the Obidi Action) is expressed as:

[math]\displaystyle{ I_{Obidi} = \int d^4x \, \sqrt{-g(S)} \left[ \tfrac{\chi}{2} (\nabla S)^2 - V(S) + \mathcal{J}(S, \phi) \right], }[/math]

where:

• [math]\displaystyle{ (\nabla S)^2 }[/math] is the kinetic term of entropy,
• [math]\displaystyle{ V(S) }[/math] is an entropy potential,
• [math]\displaystyle{ \mathcal{J}(S, \phi) }[/math] encodes universal coupling between entropy and matter fields [math]\displaystyle{ \phi }[/math],
• [math]\displaystyle{ \chi }[/math] is an entropic coupling constant.

The variational principle:

[math]\displaystyle{ \delta I_{Obidi} = 0 }[/math]

yields the Master Entropic Equation(MEE):

[math]\displaystyle{ \Box S - \frac{dV}{dS} + \frac{\partial \mathcal{J}}{\partial S} = 0, }[/math]

which governs the dynamics of entropy as a universal field.

Components of the Obidi Action

The Obidi Action contains three essential components:

1. Kinetic Entropy Term [math]\displaystyle{ (\nabla S)^2 }[/math], describing entropy gradients.
2. Potential Term [math]\displaystyle{ V(S) }[/math], defining equilibrium or attractor states.
3. Coupling Term [math]\displaystyle{ \mathcal{J}(S, \phi) }[/math], establishing universal entropy-matter coupling.

These components ensure that entropy not only constrains but also actively generates the laws of physics.

Theoretical Context

The Obidi Action belongs to the broader Theory of Entropicity (ToE), which aims to:

• Derive gravity as an entropic effect rather than a curvature of spacetime.
• Integrate physics and information theory by treating systems as entropic information processes.
• Provide an entropic explanation of consciousness, inspired by Hoffman’s Consciousness Realism, in which conscious perception is the interface of entropic dynamics.

Through this context, the Obidi Action bridges physical law, information geometry, and the phenomenology of awareness.

Philosophical Implications

The introduction of the Obidi Action carries deep conceptual implications:

• Beyond Geometry: Spacetime is not fundamental but emergent from entropy flows.
• Unified Ontology: Matter, energy, and information are different manifestations of the entropy field.
• Consciousness and Physics: Consciousness is positioned as a physical process directly linked to entropy constraints and flows.

Conclusion

The Obidi Action represents a bold rethinking of the foundations of physics. By elevating entropy to the status of the primitive field and employing a variational principle, it generates the Master Entropic Equation (MEE), providing a pathway to unify gravity, quantum mechanics, thermodynamics, and consciousness under the Theory of Entropicity(ToE).

References

• Obidi, J. O. (2025). Theory of Entropicity (ToE): Foundational Papers. Cambridge University.
• Hoffman, D. (2019). The Case Against Reality: How Evolution Hid the Truth from Our Eyes. W.W. Norton.
• Padmanabhan, T. (2010). Thermodynamical Aspects of Gravity: New insights. Reports on Progress in Physics, 73(4).
• Verlinde, E. (2011). On the Origin of Gravity and the Laws of Newton. Journal of High Energy Physics, 2011(4).