How the Local Obidi Action (LOA) of the Theory of Entropicity (ToE) Reframes Entropy as the Architect of Reality: A New Path in Modern Theoretical Physics
How the Local Obidi Action Reframes Entropy as the Architect of Reality: A New Path in Theoretical Physics
For more than a century, entropy has remained one of the most misunderstood yet powerful concepts in physics. In thermodynamics it measures disorder, in information theory it measures uncertainty, and in quantum mechanics it encodes the structure of states and entanglement. But in every context, entropy has always played a secondary role—an outcome of physical laws, not their origin.
The Theory of Entropicity (ToE) radically departs from this tradition by placing entropy not at the periphery but at the center of physical law. Its foundational principle is simple yet transformative: entropy is a fundamental field, and its geometry gives rise to the phenomena we call space, time, matter, and gravitation. This conceptual shift leads naturally to a variational framework unlike anything previously attempted—the Local Obidi Action (LOA) and its companion, the Spectral Obidi Action (SOA).
What makes these actions so remarkable is not merely the claim that entropy underlies physical reality, but the mathematical way they accomplish this. For the first time, diverse and seemingly unrelated geometric structures—Fisher–Rao, Fubini–Study, Amari–Čencov α-connections, Tsallis and Rényi entropies, and even Araki’s relative entropy—appear together within a single coherent physical action. This is not a collage of mathematical fragments; it is a unified architecture grounded in the inherent geometry of entropy itself.
Medium readers familiar with general relativity or quantum mechanics may wonder how such disparate tools can coexist inside one theory. The answer lies in understanding what happens the moment entropy becomes a field defined over spacetime rather than a passive numerical descriptor. Once entropy is treated as a fundamental dynamical entity, the geometry that naturally accompanies it is not Riemannian in the traditional sense, but informational. Variations of entropy are variations of distinguishability, coherence, and statistical structure, and these are precisely the objects measured by Fisher–Rao and Fubini–Study metrics. Likewise, the asymmetry and irreversibility of entropy flow are captured by the Amari α-connections. These structures were never designed for gravitational theories because the communities that developed them were not attempting to describe gravity. Yet when ToE reinterprets entropy as the foundational physical field, these tools reveal themselves as the natural geometric language for its dynamics.
This is the conceptual engine behind the Local Obidi Action. The LOA does not bolt together unrelated geometries; it elevates the full informational geometry of entropy into the role traditionally played by spacetime geometry. In this new picture, the entropic metric becomes the stage on which physics unfolds. In some limits it reduces to Fisher–Rao, where classical uncertainties dominate; in quantum-coherent regimes it aligns with Fubini–Study; and across irreversible processes it carries the dualistic imprint of Amari’s α-connections. Generalized entropies—Tsallis, Rényi, and even Araki’s modular entropy—appear as different deformations of this composite entropic geometry. Instead of competing definitions of entropy, ToE unifies them as different aspects of the same underlying field.
What makes this construction even more striking is that no previous program in physics has attempted anything similar. Researchers working in emergent gravity frameworks typically treat entropy as a thermodynamic constraint that reacts to geometry, not a field that generates it. Mathematicians in information geometry rarely venture into gravitational or field-theoretic territory. Quantum information theorists study Fubini–Study geometry and modular operators without interpreting them as candidates for physical curvature. In every case, the work is rigorous, but the motivation remains either statistical or quantum-informational, not cosmological or gravitational.
ToE breaks this boundary by drawing together ideas that previously lived in separate intellectual universes. The unification does not arise from mathematical novelty—Fisher–Rao and Fubini–Study metrics are decades old—but from a new physical principle: entropy is not an emergent descriptor; it is the foundational substance of the universe. Once this principle is adopted, the Local Obidi Action becomes a natural consequence rather than an eclectic choice.
The Spectral Obidi Action pushes this idea even further by translating Araki’s relative entropy—a concept previously confined to the realm of operator algebras and quantum information—into a global variational principle. ToE is the first known theoretical framework to treat Araki entropy not as a diagnostic quantity but as a generator of physical dynamics. This marks a conceptual turning point. It means that modular operators, spectral data, and the deep structure of quantum information become active participants in shaping spacetime and its evolution. The SOA introduces non-local and global constraints that complement the local differential structure of the LOA, forming a two-tier variational architecture unparalleled in the current literature.
The originality of the Obidi Actions comes not from inventing new mathematical objects but from understanding that existing structures gain profound physical meaning when entropy is recognized as the principal field of nature. From this vantage point, the diversity of generalized entropies is not a theoretical nuisance but a reflection of entropy’s multidimensional geometric character. The richness of information geometry is not a mathematical curiosity but the true geometric signature of the universal entropic field.
For the first time, these elements—classical and quantum, reversible and irreversible, local and spectral—find their place within a single unified theory. The Local Obidi Action becomes the differential engine of entropic dynamics, while the Spectral Obidi Action becomes the global regulator of consistency across the entire entropic manifold. Together, they outline a new foundation for physics in which entropy does not merely measure the state of the universe but constructs it.
If the history of physics teaches anything, it is that conceptual breakthroughs often happen when familiar ideas are reinterpreted under new principles. Just as Einstein reimagined spacetime through the lens of relativity, and Feynman reimagined quantum behavior through path integrals, ToE offers a reimagining of entropy as the architect of reality. Whether this framework becomes a cornerstone of future theoretical physics remains to be seen, but its conceptual depth and mathematical boldness mark it as one of the most intriguing developments of the modern era.
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