Uncertainty relations for arbitrary currents in coherent transport

We derive thermodynamic and kinetic uncertainty relations valid for arbitrary currents in coherent, strongly coupled, linear systems out of equilibrium. Exploiting properties of the transport statistics, in particular fluctuation theorems, we identify the relevant entropy production and activity that determine the cost of precision at the level of individual scattering events. The resulting bounds include higher-order fluctuations and remain valid far from equilibrium. We illustrate our results in normal and superconducting hybrid structures, and show that their predictiveness and validity range exceeds existing formulations.