  We develop a generalized grand canonical potential for the ballistic
nonequilibrium electron distribution in a metal nanowire with a finite applied
bias voltage. Coulomb interactions are treated in the self-consistent Hartree
approximation, in order to ensure gauge invariance. Using this formalism, we
investigate the stability and cohesive properties of metallic nanocylinders at
ultrahigh current densities. A linear stability analysis shows that metal
nanowires with certain {\em magic conductance values} can support current
densities up to 10^11 A/cm^2, which would vaporize a macroscopic piece of
metal. This finding is consistent with experimental studies of gold nanowires.
Interestingly, our analysis also reveals the existence of reentrant stability
zones--geometries that are stable only under an applied bias.
