A deformed exponential family of states on a von Neumann algebra is constructed for one specific deformation which makes the exponential function asymptotically linear. Difficulties arising due to non-commutativity are highlighted.

中文翻译：

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量子统计流形：线性增长案例

冯诺依曼代数上的变形指数状态族是为一个特定的变形构造的，这使得指数函数渐近线性。突出显示了由于非交换性引起的困难。