The Donkey on the Edge Vol. I · The Evolution · Paper I · Result II May MMXXVI
The Donkey on the Edge
Result the Second

Product class scaling

For bulk states drawn from the product class, entropy disagreement scales as 0.798 times d_B to the negative one-half power. The prefactor is analytic, not fit to data. Simulations match to under half a standard deviation at every test point.

Theorem 4.2Product ClassExact Prefactor

Two Ways of Reading the Same Finding

Paper Voice

For bulk states drawn from the product class (rank-1 density matrices), the entropy disagreement scales as:

ESASB0.798dB1/2+O(dB1)\mathbb{E}|S_A - S_B| \approx 0.798 \cdot d_B^{-1/2} + \mathcal{O}(d_B^{-1})

The prefactor 0.798 is analytic. It is not fit to data. It comes out of the math. Simulations matched the prediction to under half of one standard deviation at every test point.

Donkey Voice

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 ›
See also