Correlation-Driven Emergence of Geometry, Gravity, and Black Hole Thermodynamics

This work presents a unified theoretical framework in which spacetime geometry, gravitational dynamics, quantum evolution, and cosmological expansion emerge from a single underlying principle: the conservation and redistribution of correlation. The fundamental relation C_acc + S = C_0 encodes the balance between accessible correlation and entropy. A key development in this version is the explicit separation of entropy into global and local components. The global component defines a universal arrow of time and gives rise to the cosmological constant, while the local component governs curvature through entropy gradients and determines the stress-energy tensor. Within this framework, the Einstein field equations emerge as an effective description of correlation dynamics, with the cosmological constant interpreted as the global rate of entropy increase and matter fields arising from local redistribution of correlation. Proper time is reinterpreted as a local response to a universal temporal flow. Quantum evolution is described by a Lindblad equation derived from correlation loss, establishing a direct connection between decoherence, entropy growth, and spacetime curvature. Cosmologically, expansion is driven exclusively by global entropy increase, while local dynamics do not contribute to the global entropy budget. Dark matter and dark energy are interpreted as complementary aspects of correlation conservation, providing a natural explanation for their comparable magnitudes in the present epoch. Vacuum energy is reinterpreted as global entropy production, while local quantum fluctuations are shown not to gravitate effectively. The framework preserves the leading-order predictions of general relativity while introducing subleading corrections, including modifications to orbital precession, light bending, and black hole shadow size. This version introduces a refined formulation of the field equations with a global/local entropy split, resolves conceptual inconsistencies in the cosmological sector, and strengthens the connection between gravitational, quantum, and thermodynamic phenomena.