  The interstellar medium (ISM) is subject, on one hand, to heating and cooling
processes that tend to segregate it into distinct phases due to thermal
instability (TI), and on the other, to turbulence-driving mechanisms that tend
to produce strong nonlinear fluctuations in all the thermodynamic variables. In
this regime, large-scale turbulent compressions in the stable warm neutral
medium (WNM) dominate the clump-formation process rather than the linear
developent of TI. Cold clumps formed by this mechanism are often bounded by
sharp density and temperature discontinuities, which however are not contact
discontinuities as in the classical 2-phase model, but rather "phase transition
fronts", across which there is net mass and momentum flux from the WNM into the
clumps. The clumps grow mainly by accretion through their boundaries, are in
both thermal and ram pressure balance with their surroundings, and are
internally turbulent as well, thus also having significant density fluctuations
inside. The temperature and density of the cold and warm gas around the phase
transition fronts fluctuate with time and location due to fluctuations in the
turbulent pressure. Moreover, shock-compressed diffuse unstable gas can remain
in the unstable regime for up to a few Myr before it undergoes a phase
transition to the cold phase. These processes populate the classically
forbidden density and temperature ranges. Since gas at all temperatures appears
to be present in bi- or tri-stable turbulence, we conclude that the word
"phase" applies only locally, surrounding phase transition sites in the gas.
Globally, the word "phase" must relax its meaning to simply denote a certain
temperature or density range.
