  Perturbative corrections to General Relativity alter the expressions for both
the entropy of black holes and their extremality bounds. We prove a universal
relation between the leading corrections to these quantities. The derivation is
purely thermodynamic and the result also applies beyond the realm of
gravitational systems. In scenarios where the correction to the entropy is
positive, our result proves that the perturbations decrease the mass of
extremal black holes, when holding all other extensive variables fixed in the
comparison. This implies that the extremality relations of a wide class of
black holes display Weak Gravity Conjecture-like behavior.

High Energy Physics - Theory;General Relativity and Quantum Cosmology