关于连续熵的说明

Pub Date : 2024-01-30 DOI:10.4310/pamq.2023.v19.n5.a5

Roberto Longo, Edward Witten

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引用次数: 0

摘要

冯-诺依曼熵可以自然扩展到任意半有限冯-诺依曼代数的情况，正如 I. E. Segal 所考虑的那样。我们将这一熵与相对熵联系起来，并证明包含冯-诺依曼因子的熵增加受琼斯指数对数的约束。如果因子是无限维的，那么这个界限就是最佳的。

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A note on continuous entropy

Von Neumann entropy has a natural extension to the case of an arbitrary semifinite von Neumann algebra, as was considered by I. E. Segal. We relate this entropy to the relative entropy and show that the entropy increase for an inclusion of von Neumann factors is bounded by the logarithm of the Jones index. The bound is optimal if the factors are infinite dimensional.

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