For bulk states drawn from the Haar class (uniformly random pure states), entropy disagreement scales as 0.608 times d_B to the negative three-halves power. The prefactor is analytic. This is the regime relevant to black hole interiors.
For bulk states drawn from the Haar class (uniformly random pure states), the entropy disagreement scales as:
The prefactor 0.608 is analytic. No fitting. Simulations match. This is the regime relevant to black hole interiors and holographic codes for chaotic quantum dynamics.
A plain-language companion to the result above, in the Donkey voice. The full essay lives in the field notes; this column carries the short version.
The G-chord / symphony analogy, full essay ›