A microscopic understanding of fast ionic transport is fundamental to design novel solid-state electrolytes. We address the role of correlations in these systems and study in detail the tracer and charge diffusion coefficients, deriving a novel inequality between these two quantities. We investigate the failure of the Nernst-Einstein and the physical consequences of a nontrivial Haven ratio with extensive first-principles molecular dynamics in the fast ion conductor Li10GeP2S12. Last, we show that the approximate tracer diffusion still provides accurate activation free energies.