 00386 Daniele Guido, Roberto Longo
 Natural Energy Bounds in Quantum Thermodynamics
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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 betasubexponentially; a property which is similar in the form and weaker in the spirit than the modular compactnessnuclearity 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 BisognanoWichmann property. In general, the boundedness condition is equivalent to a holomorphic property closely
related to the one recently considered by Ruelle and D'AntoniZsido and shared by a natural class of nonequilibrium steady states. Our holomorphic property is stronger than the Ruelle's one and thus selects a restricted class of nonequilibrium 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 PuszWoronowicz complete passivity property, hence to the KMS equilibrium condition.
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