Planckian bounds from local uncertainty relations

We introduce “local uncertainty relations” in thermal quantum many-body systems from which fundamental bounds can be derived. These inequalities imply rigorous universal non-relativistic speed limits (independent of interaction range) and, as we focus on in the current work, bounds associated with transport (e.g., the diffusion constant and shear viscosity). Using the chaos bounds and other considerations, we introduce simplified non-rigorous universal transport coefficient inequalities and compare our resulting bounds against experimental data.