New insights on mutual information in the island approach to the Page curve
Abstract
In this article, we have presented one of the very important observations, regarding the behavior of mutual information of two different sets of subsystems in the after Page time scenario. This provides us with some deep insights about the redistribution of geometrical correlation between the two different sets of subsystems on a Cauchy slice. In our earlier works, we have shown how the saturation of mutual information between two specific subsystems plays a vital role in obtaining the correct Page curve for the eternal black hole. In those works, we have shown that the mutual information between B+ and B-, that is, I(B+: B−), vanishes at scrambling time, which leads to the correct Page curve. That means that at scrambling time, there is no correlation between B+ and B-. Remarkably, it is observed that at this particular value of observer's time, the mutual information between ℐ and R, that is, I(ℐ:R), becomes singular. This indicates that the regions ℐ and R become maximally entangled. This provides us with a notion of the transfer of geometric correlation between different regions on the Cauchy slice. In this work, we have also provided a way to calculate the tripartite mutual information of regions ℐ,~R+ and R-, that is, I(ℐ:R+:R-) on the Cauchy slice using the earlier results involving the bipartite regions. This is a new result which was missing in the earlier literature.
Versions
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BibTeX
@misc{chowdhury2026insights,
title = {{New insights on mutual information in the island approach to the Page curve}},
author = {Anirban Roy Chowdhury and Souvik Paul and Sunandan Gangopadhyay},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.04706},
eprint = {2607.04706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04706},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New insights on mutual information in the island approach to the Page curve
AU - Anirban Roy Chowdhury
AU - Souvik Paul
AU - Sunandan Gangopadhyay
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2607.04706
UR - https://arxiv.org/abs/2607.04706
AB - In this article, we have presented one of the very important observations, regarding the behavior of mutual information of two different sets of subsystems in the after Page time scenario. This provides us with some deep insights about the redistribution of geometrical correlation between the two different sets of subsystems on a Cauchy slice. In our earlier works, we have shown how the saturation of mutual information between two specific subsystems plays a vital role in obtaining the correct Page curve for the eternal black hole. In those works, we have shown that the mutual information between B_+ and B_-, that is, I(B_+: B_−), vanishes at scrambling time, which leads to the correct Page curve. That means that at scrambling time, there is no correlation between B_+ and B_-. Remarkably, it is observed that at this particular value of observer's time, the mutual information between ℐ and R, that is, I(ℐ:R), becomes singular. This indicates that the regions ℐ and R become maximally entangled. This provides us with a notion of the transfer of geometric correlation between different regions on the Cauchy slice. In this work, we have also provided a way to calculate the tripartite mutual information of regions ℐ,~R_+ and R_-, that is, I(ℐ:R_+:R_-) on the Cauchy slice using the earlier results involving the bipartite regions. This is a new result which was missing in the earlier literature.
ER -