Field-dependent conductivities of electrolyte solutions from generalized fluctuation-dissipation relations

We derive a relationship for the electric field dependent ionic conductivity for an electrolyte solution in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength and implicit solvent conditions. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian and subsequently the conductivity is constant with applied field. In weaker electrolytes, we find the fluctuations of the ionic current are strongly non-Gaussian and the conductivity increases with applied field, saturating to the strong electrolyte limit at large applied field. This nonlinear behavior, known phenomenologically as the Onsager-Wien effect, results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady-state.