Information Scrambling — OTOC & Quantum Chaos Bound

Out-of-time-order correlators (OTOCs) measure how quantum information spreads across a many-body system: C(t) = −⟨[W(t), V(0)]²⟩. In chaotic systems, C(t) grows exponentially as e^{λt} before saturating, where λ ≤ 2πk_BT/ℏ is the Maldacena-Shenker-Stanford (MSS) bound on quantum chaos — saturated only by black holes and the Sachdev-Ye-Kitaev (SYK) model.

0.50
3.14
2.00
MSS bound λ_max = 2π/β
λ / λ_max ratio
Butterfly velocity v_B