  We study the non-equilibrium dynamics of lipid membranes with proteins that
actively pump ions across the membrane. We find that the activity leads to a
fluctuating force distribution due to electrostatic interactions arising from
variation in dielectric constant across the membrane. By applying a multipole
expansion we find effects on both the tension and bending rigidity dominated
parts of the membranes fluctuation spectrum. We discuss how our model compares
with previous studies of force-multipole models.
