量子热力学中的自然能界
Natural Energy Bounds in Quantum Thermodynamics
摘要：
给定一个非对易流的定态，我们研究了一个有界性条件，取决于一个正参数β，这是弱于KMS平衡条件在逆温度β。这个条件相当于一个全纯性质密切相关的一个最近考虑的Ruelle和D 'Antoni-Zsido和共享的一个自然类的非平衡稳态。我们的全纯性质是强于Ruelle的一个，从而选择一个限制类的非平衡稳态。我们还介绍了完整的有界性条件，并表明这一概念是等价的Pusz-Woronowicz完整的被动属性，因此KMS条件。在量子场论中，β-有界性条件可以解释为局域化的状态向量具有以β-次指数方式增加的能量密度水平的性质，该性质在形式上与模紧性-核性条件相似，但在精神上比模紧性-核性条件弱。特别地，对于闵可夫斯基时空上的C* 代数的庞加莱协变网，当β大于2 π时，提升的β有界性被证明等价于Bisognano-Wichmann性质。因此，在β-全纯态类中，在Rindler黑洞背景下的量子系统的霍金温度是最小的。更一般地，关于Killing演化与一类静态量子黑洞，我们描述KMS热平衡态在霍金温度下的有界性性质和平移对称性的存在。
英文摘要：
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.
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