  In this paper we present a new derivation of the $H$-theorem and the
corresponding collisional equilibrium velocity distributions, within the
framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in
our derivation we do not assume any modification on the functional form of
Boltzmann's original "molecular chaos hypothesis". Rather, we explicitly
introduce into the collision scenario, the existence of statistical dependence
between the molecules before the collision has taken place, through a
conditional distribution $f(\vec{v}_2|\vec{v}_1)$. In this approach, different
equilibrium scenarios emerge depending on the value of the nonextensive
entropic parameter.
