Speaker
Description
The thermodynamic emergence of local spacetime dynamics is inextricably tied to the strict extensivity of the holographic area law. While quantum gravity candidates often motivate generalized, non-extensive entropy-area relations for black holes, substituting these into Jacobson's framework to derive modified gravity theories is generically inconsistent. We argue that any departure from holographic extensivity introduces long-range correlations that destroy local spacetime causality. Consequently, the resulting macroscopic theories inevitably violate the Equivalence Principle, break diffeomorphism invariance, or exhibit overt acausality. We conclude that an extensive area law is a necessary condition for consistent local gravitational dynamics.