  The theory of transport phenomena in multicomponent electrolyte solutions is
presented here through the integration of continuum mechanics,
electromagnetism, and non-equilibrium thermodynamics. The governing equations
of irreversible thermodynamics, including balance laws, Maxwell's equations,
internal entropy production, and linear laws relating the thermodynamic forces
and fluxes, are derived. Green-Kubo relations for the transport coefficients
connecting electrochemical potential gradients and diffusive fluxes are
obtained in terms of the flux-flux time correlations. The relationship between
the derived transport coefficients and those of the Stefan-Maxwell and
infinitely dilute frameworks are presented, and the connection between the
transport matrix and experimentally measurable quantities is described. To
exemplify application of the derived Green-Kubo relations in molecular
simulations, the matrix of transport coefficients for lithium and chloride ions
in dimethyl sulfoxide is computed using classical molecular dynamics and
compared with experimental measurements.

Statistical Mechanics;Soft Condensed Matter;Fluid Dynamics