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Relative entropy is a non-negative quantity and depicts a difference between two probability distributions. In this talk, I explain constraints on perturbative corrections to the Euclidean effective action by the relative entropy. I show that the relative entropy can yield the constraints on some effective field theories generated by a class of UV theories with a specific sign of interactions between heavy and light degrees of freedom. For such a class of theories, I show that the interactions increase thermodynamic entropy at fixed energy and charge, which is connected with the extremality relations of black holes exhibiting Weak-Gravity-Conjecture.