  Fluidity, the ability of liquids to flow, is the key property distinguishing
liquids from solids. This fluidity is set by the mobile transit atoms moving
from one quasi-equilibrium point to the next. The nature of this transit motion
is unknown. Here, we show that flow-enabling transits form a dynamically
distinct sub-ensemble where atoms move on average faster than the overall
system, with a manifestly non-Maxwellian velocity distribution. This is in
contrast to solids and gases where no distinction of different ensembles can be
made and where the distribution is always Maxwellian. The non-Maxwellian
distribution is described by an exponent $\alpha$ corresponding to high
dimensionality of space. This is generally similar to extra synthetic
dimensions in topological quantum matter, albeit higher dimensionality in
liquids is not integer but is fractional. The dimensionality is close to 4 at
melting and exceeds 4 at high temperature. $\alpha$ has a maximum as a function
of temperature and pressure in liquid and supercritical states, returning to
its Maxwell value in the solid and gas states.
