A note on continuous entropy
Mathematical Physics
2022-02-08 v1 High Energy Physics - Theory
math.MP
Operator Algebras
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.
Keywords
Cite
@article{arxiv.2202.03357,
title = {A note on continuous entropy},
author = {Roberto Longo and Edward Witten},
journal= {arXiv preprint arXiv:2202.03357},
year = {2022}
}
Comments
18 pages