Electromagnetic Time Lags in Compact Mergers from Entropic Geometry

We propose Entropic Geometry, a foundational framework in which spacetime dynamics emerge from the constrained coupling between energy and causal information. Physical states are characterized by the tuple $\Psi=\{E, S\}$, where $S$ denotes realized causal information, and a conservation law is imposed on total processing capacity. From this principle, we show that General Relativity arises as the thermodynamic, coarse-grained limit of information optimization. Within this framework, the gravitational constant $G$ is identified as a derived parameter determined by the vacuum impedance $\xi$, which depends on local information density. This scale dependence reproduces standard Newtonian gravity in high-acceleration regimes while yielding MOND-like phenomenology ($a