Maximal entangling rates from holography

We prove novel far-from-equilibrum bounds on conformal field theories, upper bounding the growth rate of entanglement entropy in spatially uniform states. When equal-time correlators and Wilson loops are computed by geodesics and world sheets, we also bound the growth rate of these. Example applications include lower bounds on thermalization times or the time it takes to achieve deconfinement. Our bounds are proven for holographic conformal field theories at strong coupling and large-N, but we provide evidence that they are valid independent of these assumptions. In two dimensions, our results prove a conjectured bound on entanglement growth by Liu and Suh for a large class of states. We also derive bounds on spatial derivatives of correlation measures. From a gravitational perspective, our results constitute new lower bounds on the mass of asymptotically AdS spacetimes with planar symmetry, strengthening the positive mass theorem for these spacetimes. We also derive novel relations in AdS=CFT relating various geometric features directly to entanglement entropy derivatives. For example, we show that conformal field theory entanglement growth corresponds to bulk matter falling deeper into the bulk.