Phys. Rev. Lett. (in the press); preprint at

In relativistic systems, information propagation is bounded by the speed of light, giving rise to the light-cone structure in Minkowski spacetime. A similar constraint exists in non-relativistic local quantum spin systems, known as the Lieb–Robinson bound. This provides a maximum propagation speed of entanglement and correlation, in turn leading to an effective spacetime light-cone. Now Thomas Hartman and colleagues have shown that consistency of diffusive transport with this light-cone places an upper bound on diffusivity.

Relating three independent quantities — diffusivity, equilibration timescale and light-cone velocity — this upper bound is found to hold in a variety of physical systems in both regimes of strong and weak coupling. The result has wide implications, including a generalization of the Drude formula giving the lower bound of electrical resistivity in the absence of long-lived quasiparticles, and a relation between hydrodynamic and leading non-hydrodynamic modes in black holes. It will also motivate more systematic studies — for example, using ultracold quantum gases and unconventional metals, for simultaneous determination of the three quantities involved in setting the bound.