A note on continuous entropy

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI:10.4310/pamq.2023.v19.n5.a5

Roberto Longo, Edward Witten

引用次数: 0

Abstract

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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关于连续熵的说明

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.