The Bekenstein-Hawking entropy state counting and the Page curve for Hawking radiation entanglement entropy are equivalent from the gravity path integral viewpoint via a convex optimization problem for von Neumann entropy.
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State counting in gravity and maximal entropy principle
The Bekenstein-Hawking entropy state counting and the Page curve for Hawking radiation entanglement entropy are equivalent from the gravity path integral viewpoint via a convex optimization problem for von Neumann entropy.