  Seemingly unrelated experiments such as electrolyte transport through
nanotubes, nano-scale electrochemistry, NMR relaxometry and Surface Force
Balance measurements, all probe electrical fluctuations: of the electric
current, the charge and polarization, the field gradient (for quadrupolar
nuclei) and the coupled mass/charge densities. The fluctuations of such various
observables arise from the same underlying microscopic dynamics of the ions and
solvent molecules. In principle, the relevant length and time scales of these
dynamics are encoded in the dynamic structure factors. However modelling the
latter for frequencies and wavevectors spanning many orders of magnitude
remains a great challenge to interpret the experiments in terms of physical
process such as solvation dynamics, diffusion, electrostatic and hydrodynamic
interactions between ions, interactions with solid surfaces, etc. Here, we
highlight the central role of the charge-charge dynamic structure factor in the
fluctuations of electrical observables in electrolytes and offer a unifying
perspective over a variety of complementary experiments. We further analyze
this quantity in the special case of an aqueous NaCl electrolyte, using
simulations with explicit ions and an explicit or implicit solvent. We discuss
the ability of the standard Poisson-Nernst-Planck theory to capture the
simulation results, and how the predictions can be improved. We finally discuss
the contributions of ions and water to the total charge fluctuations. This work
illustrates an ongoing effort towards a comprehensive understanding of
electrical fluctuations in bulk and confined electrolytes, in order to enable
experimentalists to decipher the microscopic properties encoded in the measured
electrical noise.
