  Using molecular simulation, we assess the impact of an electric field on the
properties of water, modeled with the SPC/E potential, over a wide range of
states and conditions. Electric fields of the order of $0.1V/$\AA and beyond
are found to have a significant impact on the grand-canonical partition
function of water, resulting in shifts in the chemical potential at the
vapor-liquid coexistence of up to $20$%. This, in turn, leads to increases in
the critical temperatures by close to $7$% for a field of $0.2V/$\AA, to lower
vapor pressures, and to much larger entropies of vaporization (by up to $35$%).
We interpret these results in terms of the greater density change at the
transition and of the increased structural order resulting from the applied
field. The thermodynamics of compressed liquids and of supercritical water are
also analyzed over a wide range of pressures, leading to the determination of
the Zeno line and of the curve of ideal enthalpy that span the supercritical
region of the phase diagram. Rescaling the phase diagrams obtained for the
different field strength by their respective critical properties allows us to
draw a correspondence between these systems for fields of up to $0.2V/$\AA.
