An entropy bound due to symmetries

2024/01/04 by Roberto Longo, Longo, Roberto, Vincenzo Morinelli +1 · 1 citation
Mathematics · #46L60 #81P45 #81T05 #81T40 #94A17 #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.02345

openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime ℝ^d+1, covariant with respect to a positive energy, unitary representation U of the Poincaré group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy S_H(ϕ| | C) of a vector in a region C that depends only on U and the PCT anti-unitary canonically associated with H. A similar result holds for local, Möbius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the U(1)-current derivatives.

Cited by

• The modular Hamiltonian in asymptotically flat spacetime conformal to Minkowski

Related

• Local entropy theory and applications
• A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC
• The Problem of Positive Kolmogorov-Sinai entropy for the Standard map
• Finite dimensions and the covariant entropy bound
• Area Law for Localization-Entropy in Local Quantum Physics