  Maxwell's velocity distribution is known to be universally valid across
systems and phases. Here we present a new and general derivation that uses the
central limit theorem (CLT) of the probability theory. This essentially uses
the idea that repeated intermolecular collisions introduce randomness in the
velocity change in the individual components of the velocity vector, leading
to, by the CLT, a Gaussian distribution. To complete the derivation, we next
show that the mean-square velocity or the standard deviation follows exactly
from Boltzmann's formula relating entropy to the density of states, thus
avoiding the use of the ideal gas equation of state explicitly. We furthermore
prove the Maxwell velocity distribution for a system of harmonic oscillators.
This derivation provides a further insight into the origin of Boltzmann's
constant in the Maxwell velocity distribution and also in the equipartition
theorem. We propose that this derivation provides an approach that explains the
universality of Maxwell Gaussian distribution.
