To gain a deeper understanding of the microscopic electrostatic properties of aqueous solutions, we study the fluctuations in the Madelung potential. We quantify these fluctuations in terms of probability distribution functions, P (U α ). The equilibrium probability distribution functions, P (U α ) bulk , for α =Na + and Cl -for a periodically replicated bulk system with the same force field and electrolyte concentration are plotted in Fig. . These distributions indicate that fluctuations in U i are roughly Gaussian with means of ⟨U Na+ ⟩ ≈ -8.5V and ⟨U Cl-⟩ ≈ 8.5V and variances of ⟨(δU i ) 2 ⟩ Na+ ≈ 0.22 and ⟨(δU i ) 2 ⟩ Cl-≈ 0.19. The differences in these means and variances arise due to differences in the solvation structure of the two different ionic species. The values of ⟨U α ⟩ differ from those presented in Fig. , because the long range nature of Coulomb interaction causes these values to depend on the details of the simulation cell (periodic versus interfacial).