Why do we require Boltzmann equation to be applicable for only dilute regime? Why do we force the assumption for Boltzmann Equation to be dilute?
Is there any exact formula that defines this DILUTE? and why it has to be dilute? Does it has anything to do with mean free path?
(If a gas mixture is so diluted that particles in the gas are to a good approximation not statistically correlated, then singlet distribution functions are sufficient for description of the macroscopic behavior of the gas?? For this explanation, it is quite vague.)
I did not find anything on net or wiki about this.
By the way, if it is initially used to describe gas systems, then why is it also used to describe liquid? It is quite strange since a liguid is not dilute to my sence.
 A: According to Wikipedia
one of the assumptions for the applicability
of the kinetic theory of gases is:

The gas consists of very small particles known as molecules.
   This smallness of their size is such that the total volume
   of the individual gas molecules added up is negligible
   compared to the volume of the smallest open ball containing
   all the molecules. This is equivalent to stating that the
   average distance separating the gas particles is large
   compared to their size.

This is a much more precise definition instead of just saying
the gas is dilute.
Another equivalent way to define a dilute gas can be:
Most of the time the gas molecules move undisturbed by
the other molecules (i.e. in straight lines, with constant velocity).
Only in a very small fraction of time (during collisions)
they get disturbed by other molecules.

For dense gases (and even more for liquids) you need to
consider several things, which were neglectable for dilute gases:


*

*You need to account for the volume occupied by
the molecules themselves.

*You need to account for the potential energy
between molecules when they are colliding.

*You need to distinguish between bosons and fermions,
i.e. use the Bose-Einstein or Fermi-Dirac distribution respectively,
instead of the Boltzmann distribution.

