Operator size at finite temperature and Planckian bounds on quantum dynamics

Understand

It has long been believed that dissipative time scales $\tau$ obey a "Planckian" bound $\tau \gtrsim \frac{\hbar}{k_{\mathrm{B}}T}$ in strongly coupled quantum systems.

• Despite much circumstantial evidence, however, there is no known $\tau$ for which this bound is universal.
• Here we define operator size at finite temperature, and conjecture such a $\tau$: the time scale over which small operators become large.
• All known many-body theories are consistent with this conjecture.