  We present a semi-rigorous justification of Bekenstein's Generalized Second
Law of Thermodynamics applicable to a universe with black holes present, based
on a generic quantum gravity formulation of a black hole spacetime, where the
bulk Hamiltonian constraint plays a central role. Specializing to Loop Quantum
Gravity, and considering the inspiral and post-ringdown stages of binary black
hole merger into a remnant black hole, we show that the Generalized Second Law
implies a lower bound on the non-perturbative LQG correction to the
Bekenstein-Hawking area law for black hole entropy. This lower bound itself is
expressed as a function of the Bekenstein-Hawking area formula for entropy.
Results of the analyses of LIGO-VIRGO-KAGRA data recently performed to verify
the Hawking Area Theorem for binary black hole merger, are shown to be entirely
consistent with this Loop Quantum Gravity-induced inequality. However, the
consistency is independent of the magnitude of the Loop Quantum Gravity
corrections to black hole entropy, depending only on the negative algebraic
sign of the quantum correction. We argue that results of alternative quantum
gravity computations of quantum black hole entropy, where the quantum entropy
exceeds the Bekenstein-Hawking value, may not share this consistency.
