We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type II∞ von Neumann algebra. We discuss how this algebra can be coupled to the algebra of observable of an infinite reservoir within the canonical ensemble, aiming to induce nonequilibrium dynamics. The resulting dynamics can lead the system towards a nonequilibrium steady state which can be characterized through modular theory. Within this framework we address the definition of entropy production and its relationship to relative entropy, alongside exploring other applications.

中文翻译：

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关于引力代数的非平衡动力学


我们探讨了量子引力中出现的某些算子代数的非平衡特征。黑洞背景中可观察对象的代数是 II 型 ∞ von Neumann 代数。我们讨论了如何将该代数与规范集合中无限储层的可观察代数耦合，旨在诱导非平衡动力学。由此产生的动力学可以使系统走向非平衡稳态，这可以通过模理论来表征。在这个框架中，我们讨论了熵产生的定义及其与相对熵的关系，同时探索了其他应用。