  This article presents a phenomenological dynamic phase transition theory --
modeling and analysis -- for superfluids. As we know, although the
time-dependent Ginzburg-Landau model has been successfully used in
superconductivity, and the classical Ginzburg-Landau free energy is still
poorly applicable to liquid helium in a quantitative sense. The study in this
article is based on 1) a new dynamic classification scheme of phase
transitions, 2) new time-dependent Ginzburg-Landau models for general
equilibrium transitions, and 3) the general dynamic transition theory. The
results in this article predict the existence of a unstable region H, where
both solid and liquid He II states appear randomly depending on fluctuations
and the existence of a switch point M on the lambda-curve, where the
transitions changes types.
