't Hooft suppression and holographic entropy

Understand

Recent works have related the bulk first law of black hole mechanics to the first law of entanglement in a dual CFT.

• These are first order relations, and receive corrections for finite changes.
• In particular, the latter is naively expected to be accurate only for small changes in the quantum state.
• But when Newton's constant is small relative to the AdS scale, the former holds to good approximation even for classical perturbations that contain many quanta.