00-386 Daniele Guido, Roberto Longo

Natural Energy Bounds in Quantum Thermodynamics (78K, LaTeX 2e) Oct 2, 00

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Abstract. We characterize KMS thermal equilibrium states, at Hawking temperature 1/beta, for the Killing evolution associated with a class of stationary quantum black holes in terms of a boundedness property, namely the localized state vectors should 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 Quantum Field Theory. In particular, for a Poincare' covariant net of C*-algebras on the Minkowski spacetime, the boundedness property for the boosts (in the Rindler wedge) is shown to be equivalent to the Bisognano-Wichmann property. In general, the boundedness 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. The Hawking temperature is minimal for a thermodynamical system in the background of a black hole within this class of states. Given a stationary state for a noncommutative flow, 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 equilibrium condition.

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