A Unified Theory of Quantum, Thermal, and Geometric Physics from Complex Time, Information-Geometry Equivalence, and Maximum Entropy Gradient Flow

We propose a novel theoretical framework that unifies quantum mechanics, thermodynamics, and gravity through three fundamental principles: (i) Complex Time Principle, where physical processes are governed by first-order evolution on a complex time manifold; (ii) Information-Geometry Equivalence Principle, which postulates a local equality between spacetime curvature and quantum entanglement entropy density; and (iii) Maximum Entropy Gradient Principle, asserting that all dynamics follow an \ (L²\) -gradient flow of a free energy functional containing Fisher information. Three original equations encapsulate these ideas. We derive their mathematical consequences, including a fixed relation between the total entropy, total information, and the observable universe size, and present several testable predictions. The framework suggests that space and time are projections of a deeper complex structure, and that quantum coherence, thermal dissipation, and geometry are inseparable aspects of a single underlying dynamics.