A note on continuous entropy

Roberto Longo, Edward Witten

Research output: Contribution to journalArticlepeer-review


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 Neu-mann factors is bounded by the logarithm of the Jones index. The bound is optimal if the factors are infinite dimensional.

Original languageEnglish (US)
Pages (from-to)2501-2523
Number of pages23
JournalPure and Applied Mathematics Quarterly
Issue number5
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics


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