  A gap in understanding the link between continuum theories of ion transport
in ionic liquids and the underlying microscopic dynamics has hindered the
development of frameworks for transport phenomena in these concentrated
electrolytes. Here, we construct a continuum theory for ion transport in ionic
liquids by coarse graining a simple exclusion process of interacting particles
on a lattice. The resulting dynamical equations can be written as a gradient
flow with a mobility matrix that vanishes at high densities. This form of the
mobility matrix gives rise to a charging behaviour that is different to the one
known for electrolytic solutions, but which agrees qualitatively with the
phenomenology observed in experiments and simulations.
