  We define a superfluid state to be a nonequilibrium stationary state (NESS),
which, at zero temperature, satisfies certain \emph{metastability conditions},
which physically express that there should be a sufficiently small
energy-momentum transfer between the particles of the fluid and the
surroundings (e.g., pipe). It is shown that two models, the Girardeau model and
the Huang-Yang-Luttinger (HYL) model describe superfluids in this sense and,
moreover, that, in the case of the HYL model, the metastability condition is
directly related to Nozi\`{e}res' conjecture that, due to the repulsive
interaction, the condensate does not suffer fragmentation into two (or more)
parts, thereby assuring its quantum coherence. The models are rigorous examples
of NESS in which the system is not finite, but rather a many-body system.
\end{abstract}
