  Nonadditive Tsallis $q$-statistics has successfully been applied for a
plethora of systems in natural sciences and other branches of knowledge.
Nevertheless, its foundations have been severely criticised by some authors
based on the standard additive Boltzmann-Gibbs approach thereby remaining a
quite controversial subject. In order to clarify some polemical concepts, the
distribution function for an ideal gas with a finite number of point particles
and its $q$-index are analytically determined. The two-particle correlation
function is also derived. The degree of correlation diminishes continuously
with the growth of the number of particles. The ideal finite gas system is
usually correlated, becomes less correlated when the number of particles grows,
and is finally, fully uncorrelated when the molecular chaos regime is reached.
It is also advocated that both approaches can be confronted through a careful
kinetic spectroscopic experiment. The analytical results derived here suggest
that Tsallis q-statistics may play a physical role more fundamental than
usually discussed in the literature.
