Table : Self-diffusion coefficients D s (10 -2 Å2 ps -1 ) of active protons and acetate groups, the Green-Kubo conductivity σ G-K (mS cm -1 ), the Nernst-Einstein deviation ∆ = 1 -σ G-K /σ N-E obtained from MD simulations at 340 K using MLPs generated with PiNet2-P3 (abbreviated as "P3" in the ulations of 5 ns (in order to reach the diffusive regime) with the last generations of MLPs to compute transport coefficients. Following ref.