Relative-Entropy Flow Across the Page Transition
Abstract
We develop a computational framework for the quantum relative entropy based on the replica trick and apply it to analyze the evaporation process method of Jackiw-Teitelboim black holes. We show that the relative entropies between the exact radiation state and the Hawking saddle state and the replica wormholes saddle state quantify information-theoretic costs inherent to coarse-grained semiclassical descriptions. During evaporation, the relative entropy for the Hawking saddle increases monotonically, reflecting a progressively higher thermodynamic cost of sustaining the Hawking description. Conversely, the relative entropy associated with the replica wormholes saddle decreases, which indicates that the description of connected geometries becomes progressively more accurate. Moreover, the sign of the difference between the two quantities reverses precisely at the Page time, providing an information-theoretic diagnosis for the transition between competing gravitational saddles. Our results recast the Page transition as a flow of relative entropy costs between competing semi-classical descriptions, revealing an information-theoretic structure underlying the emergence of effective irreversibility in coarse-grained black hole evaporation.
Related
- Topology of Hawking-Page phase transition and equilibrium phases in AdS brane backgrounds
- Entanglement entropy across the dynamical phase transition in the quantum 𝒪(N) model
- Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory
- The Page Transition in the Multi-Time Correlations of Hawking Radiation
- Hawking-Page phase transition for pure Lovelock black holes
BibTeX
@misc{yu2026relativeentropy,
title = {{Relative-Entropy Flow Across the Page Transition}},
author = {Minghui Yu and Xian-Hui Ge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08397},
eprint = {2610.08397},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08397},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relative-Entropy Flow Across the Page Transition
AU - Minghui Yu
AU - Xian-Hui Ge
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08397
UR - https://arxiv.org/abs/2610.08397
AB - We develop a computational framework for the quantum relative entropy based on the replica trick and apply it to analyze the evaporation process method of Jackiw-Teitelboim black holes. We show that the relative entropies between the exact radiation state and the Hawking saddle state and the replica wormholes saddle state quantify information-theoretic costs inherent to coarse-grained semiclassical descriptions. During evaporation, the relative entropy for the Hawking saddle increases monotonically, reflecting a progressively higher thermodynamic cost of sustaining the Hawking description. Conversely, the relative entropy associated with the replica wormholes saddle decreases, which indicates that the description of connected geometries becomes progressively more accurate. Moreover, the sign of the difference between the two quantities reverses precisely at the Page time, providing an information-theoretic diagnosis for the transition between competing gravitational saddles. Our results recast the Page transition as a flow of relative entropy costs between competing semi-classical descriptions, revealing an information-theoretic structure underlying the emergence of effective irreversibility in coarse-grained black hole evaporation.
ER -