Deriving the Entropy Functional in <i>f(Q)</i> Gravity Consistent with Entanglement Entropy

Abstract A generalized entropy functional for gravity is derived by adapting the Noether charge formalism to the nonmetricity‐based gravitational Lagrangian. The resulting functional, generalizes the Bekenstein–Hawking law and is shown to be consistent with the first law of entanglement thermodynamics. This consistency establishes a direct link between the modification of the gravitational action and the entanglement structure of spacetime, providing a robust thermodynamic and quantum information–theoretic interpretation for gravity.