Axiomatic Unification of Quantum Mechanics, Thermodynamics, and Gravity via Complex Time, Information Geometry, and Entropic Gradient Flow

We propose a unified formal framework for quantum mechanics, thermodynamics, and gravity based on three axioms: (i) Complex Time Principle: Physical processes are described by first-order evolution on a complex time manifold, with real time corresponding to unitary quantum coherence and imaginary time to thermal dissipation. (ii) Information--Geometry Equivalence: Spacetime curvature is locally equivalent to the density of quantum entanglement entropy. (iii) Maximal Entropy Gradient Principle: The evolution of a physical system follows the \ (L²\) -gradient flow of a free energy functional that includes the quantum Fisher information. From these axioms we construct an action on a complex time contour, derive generalized Einstein equations and complex-time evolution equations, and show that the linear response limit recovers the Kubo formula and standard Einstein gravity. We propose an explicit covariant form for the information-geometric coupling term \ (₈₍₅₎\) and discuss testable predictions, including modifications to gravitational wave waveforms from entanglement entropy, imaginary-time coherence effects near black hole horizons, and geometric phases in quantum heat engines driven by Fisher information metric.