Let B be a spacetime region of width \(2R >0\) , and \(\varphi \) a vector state localized in B. We show that the vacuum relative entropy of \(\varphi \) , on the local von Neumann algebra of B, is bounded by \(2\pi R\) -times the energy of the state \(\varphi \) in B. This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.
