A Planckian Bound on Thermalization

The late-time, long distance behavior of a generic quantum many-body system at finite temperature is described by fluctuating hydrodynamics. This description is valid in the regime where the system has locally thermalized, and microscopic short-distance details have been washed out. At weak coupling, local thermalization occurs more quickly when interactions are stronger. A natural question arises: can systems locally thermalize arbitrarily quickly? By studying the consistency of fluctuating hydrodynamics at early times, we prove that systems cannot thermalize faster than the "Planckian" timescale $\hbar / T$. We also find that systems can only thermalize within a ``light-cone", with an emergent velocity fixed by the diffusion constant and temperature.