Scrambling is the process by which local quantum information spreads across a many-body system, becoming inaccessible to local measurements. Measured by out-of-time-order correlators (OTOCs), the scrambling time tells you how quickly a perturbation at one site becomes invisible at that site because the information has spread everywhere.
In critical systems — at phase transitions, where correlations are long-range — Hosho & Hamazaki (arXiv:2603.13016) show that scrambling dynamics can serve as a quantum clock. The scrambling time at a critical point scales with system size in a way that depends on the universality class — the critical exponents determine how fast information spreads, and this spreading rate is a universal quantity.
The clock works because critical systems have a natural timescale: the time for a perturbation to propagate across the correlation length. At the critical point, the correlation length diverges, and the propagation time diverges with it in a manner determined by the dynamic critical exponent z. The scrambling time inherits this divergence, but with corrections that depend on the full set of critical exponents.
This connects two usually separate areas. Quantum information theory studies scrambling as a property of the Hamiltonian's complexity. Condensed matter physics studies critical phenomena as emergent properties of many-body systems. The scrambling clock links them: the information-theoretic quantity (how fast does local information become nonlocal?) is determined by the thermodynamic universality class (which phase transition are you at?).
The practical implication: if you can measure scrambling time as a function of system size, you can extract critical exponents without measuring any thermodynamic observable. The information dynamics at a phase transition are equivalent to the thermal dynamics — they're the same physics measured in a different basis.