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A note on continuous entropy

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arxiv 2202.03357 v1 pith:AU5HZVQW submitted 2022-02-07 math-ph hep-thmath.MPmath.OA

Roberto Longo , Edward Witten This is my paper · ORCID
classification math-phhep-thmath.MPmath.OA
keywords entropyneumannfactorsalgebraarbitraryboundboundedcase
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Algebras for generalized entanglement wedges

    hep-th 2025-11 conditional novelty 7.0 of 10

    Generalized (Bousso–Penington) entanglement wedges are conjectured to carry von Neumann algebras such that S_gen(W) = S(ω|A_W) − log Ind(E) + K_Ω (eq. 2.7), making BP's monotonicity and strong subadditivity consequenc...

  2. The Crossed Product, Modular (Tomita) Dynamics and its Role in the Transition of Type $III$ to Type $II_{\infty}$ v.Neumann Algebras and Connections to Quantum Gravity

    gr-qc 2025-07 reject novelty 3.0 of 10

    A review of Takesaki crossed product duality plus an unproven conjecture that modular Hamiltonian evolution of vacuum fluctuations is the microscopic mechanism of gravitational time dilation.

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