Bound on thermalization from hydrodynamic fluctuations

Strange metal phenomenology has motivated the "Planckian bound", a conjecture that there is a universal quantum statistical mechanics limit on a suitable local equilibration time. However, it has been debated how to define this equilibration time, given that natural candidates (such as transport time or quasiparticle lifetime) seem to allow for violations of the conjectured bound. I will propose a sharp and universal definition of local equilibration time in local many-body systems as the time scale of emergence of diffusion. This definition does not rely on an underlying Boltzmann description, and applies equally well to spin chains, insulators, metals, fluids, I will then show that this time scale is bounded by the strong coupling scale of the effective field theory of diffusion. For a class of systems, this leads to the Planckian bound.