2000/10/31 by Daniele Guido, Roberto Longo · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #math-ph #math.MP #math.OA #msc:46L55 #msc:81T20 #msc:82C10
paper · pdf · doi:10.1007/s002200100416
published as Comm. Math. Phys. 218 (2001) 513-536 · 28 pages, LaTeX. Minor modifications in the abstract, to appear in Commun. Math. Phys
arxiv created 2000/12/27 · openalex publication_date 2001/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a stationary state for a noncommutative flow, we study a boundedness condition, depending on a positive parameter beta, which is weaker than the KMS equilibrium condition at inverse temperature beta. This condition is equivalent to a holomorphic property closely related to the one recently considered by Ruelle and D'Antoni-Zsido and shared by a natural class of non-equilibrium steady states. Our holomorphic property is stronger than the Ruelle's one and thus selects a restricted class of non-equilibrium steady states. We also introduce the complete boundedness condition and show this notion to be equivalent to the Pusz-Woronowicz complete passivity property, hence to the KMS condition. In Quantum Field Theory, the beta-boundedness condition can be interpreted as the property that localized state vectors have energy density levels increasing beta-subexponentially, a property which is similar in the form and weaker in the spirit than the modular compactness-nuclearity condition. In particular, for a Poincare' covariant net of C*-algebras on the Minkowski spacetime, the beta-boundedness property, for beta greater equal than 2 pi, for the boosts is shown to be equivalent to the Bisognano-Wichmann property. The Hawking temperature is thus minimal for a thermodynamical system in the background of a Rindler black hole within the class of beta-holomorphic states. More generally, concerning the Killing evolution associated with a class of stationary quantum black holes, we characterize KMS thermal equilibrium states at Hawking temperature in terms of the boundedness property and the existence of a translation symmetry on the horizon.