Volume Entropy

Valerio Astuti (1, 2) , Marios Christodoulou (2, 1) , Carlo Rovelli (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E4 Gravité quantique

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 states --with finite-volume individual 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": the von Neumann entropy associated to the measurement of volume.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Valerio Astuti, Marios Christodoulou, Carlo Rovelli. Volume Entropy. Classical and Quantum Gravity, 2019, 36 (5), pp.055012. ⟨10.1088/1361-6382/aafec7⟩. ⟨hal-01476783⟩