Local Molecular Field Theory for Nonequilibrium Systems

We provide a framework for extending equilibrium local molecular field (LMF) theory to a statistical ensemble evolving under a time-dependent applied field. In this context, the self-consistency of the original LMF equation is achieved dynamically, which provides an efficient method for computing the equilibrium LMF potential, in addition to providing the nonequilibrium generalization. As a concrete example, we investigate water confined between hydrophobic or charged walls, systems that are very sensitive to the treatment of long-ranged electrostatics. We then analyze confined water in the presence of a time-dependent applied electric field, generated by a sinusoidal or abrupt variation of the magnitudes of uniform charge densities on each wall. Very accurate results are found from the time-dependent LMF formalism even for strong static fields and for time-dependent systems that are driven far from equilibrium where linear response methods fail.