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Volume Entropy

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arxiv 1603.01561 v3 pith:3YOYKJNR submitted 2016-03-04 gr-qc

Valerio Astuti , Marios Christodoulou , Carlo Rovelli This is my paper · ORCID
classification gr-qc
keywords volumeentropydimensionspaceallowsassociatedboundedbrunnemann
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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 $V \log V$. This allows us to introduce the notion of "volume entropy" for this phase space: the von Neumann entropy associated to the measurement of volume.

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Cited by 1 Pith paper

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  1. Evolution of interior entropy of a loop quantum-corrected black hole pierced by a cosmic string

    gr-qc 2024-12 conditional novelty 4.0 of 10

    For a large-mass loop-quantum-corrected black hole pierced by a cosmic string, the paper derives the evolution relation between interior entropy and Bekenstein-Hawking entropy and shows the total satisfies the second law.

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