Volume entropy

DOI10.1088/1361-6382/AAFEC7zbMATH Open1476.83040arXiv1603.01561OpenAlexW4213305746MaRDI QIDQ3380525

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Publication date: 29 September 2021

Published in: (Search for Journal in Brave)

Abstract: Building on a technical result by Brunnemann and Rideout on the spectrum of the Volume operator in Loop Quantum Gravity, we show that the dimension of the space of the quadrivalent, diffeomorphism invariant states with no zero-volume nodes describing a region with total volume smaller than $V$, has emph{finite} dimension, bounded by $VlogV$. This allows us to introduce the notion of "volume entropy" for this phase space: the von Neumann entropy associated to the measurement of volume.

Full work available at URL: https://arxiv.org/abs/1603.01561

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