  We investigate the relationship between the mass and velocity fields of the
intergalactic medium (IGM) and dark matter. Although the evolution of the IGM
is dynamically governed by the gravity of the underlying dark matter field,
some statistical properties of the IGM inevitably decouple from those of the
dark matter once the nonlinearity of the dynamical equations and the stochastic
nature of the field is considered. With simulation samples produced by a hybrid
cosmological hydrodynamic/N-body code, which is effective in capturing shocks
and complicated structures with high precision, we find that the one-point
distributions of the IGM field are systematically different from that of dark
matter as follows: 1.) the one-point distribution of the IGM peculiar velocity
field is exponential at least at redshifts less than 2, while the dark matter
velocity field is close to a Gaussian field; 2.) although the one-point
distributions of the IGM and dark matter are similar, the point-by-point
correlation between the IGM and dark matter density fields significantly
differs on all scales and redshifts analyzed; 3.) the one-point density
distributions of the difference between IGM and dark matter fields are highly
non-Gaussian and long tailed. These discrepancies violate the similarity
between the IGM and dark matter and cannot be explained simply as Jeans
smoothing of the IGM. However, these statistical discrepancies are consistent
with the fluids described by stochastic-force driven nonlinear dynamics.
