  Molecular dynamics of two water models, SPC/E and TIP3P, at a number of
temperatures is used to test the Kivelson-Madden equation connecting
single-particle and collective dielectric relaxation times through the Kirkwood
factor. The relation is confirmed by simulations and used to estimate the
nonlinear effect of the electric field on the dielectric relaxation time. We
show that the main effect of the field comes through slowing down of the
single-particle rotational dynamics and the relative contribution of the
field-induced alteration of the Kirkwood factor is insignificant for water.
Theories of nonlinear dielectric relaxation need to mostly account for the
effect of the field on rotations of a single dipole in a polar liquid.
