Relative entropy and effective field theory

Relative entropy quantifies the difference between two probability distribution functions, which is connected with key properties of physics, such as unitarity. In this talk, one of the most attractive features of relative entropy, non-negativity, is briefly reviewed. Then, I consider the relative entropy between two theories with and without interaction between heavy and light degrees of freedom. I explain connections between the non-negativity of the relative entropy and several phenomena, e.g., the positive magnetic susceptibility in the Ising model, the positivity bounds on the SMEFT SU(N) gauge bosonic operators, etc. I also discuss constraints on higher-derivative terms of the Einstein-Maxwell theory and the limitations of the relative entropy consideration in EFTs involving gravitational effects.