A Bekenstein-Type Bound in QFT
Roberto Longo · Communications in Mathematical Physics · 2025
Abstract Let B be a spacetime region of width $$2R >0$$ 2 R > 0 , and $$\varphi $$ φ a vector state localized in B. We show that the vacuum relative entropy of $$\varphi $$ φ , on the local von Neumann algebra of B, is bounded by $$2\pi R$$ 2 π R -times the energy of the state $$\varphi $$ φ 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.