  The dynamics of QCD matter is often described using effective mean field (MF)
models based on Boltzmann-Gibbs (BG) extensive statistics. However, such matter
is normally produced in small packets and in violent collisions where the usual
conditions justifying the use of BG statistics are not fulfilled and the
systems produced are not extensive. This can be accounted for either by
enriching the original dynamics or by replacing the BG statistics by its
nonextensive counterpart described by a nonextensivity parameter $q\neq 1$ (for
$q \to 1$ one returns to the extensive situation). In this work we investigate
the interplay between the effects of dynamics and nonextensivity. Since the
complexity of the nonextensive MF models prevents their simple visualization,
we instead use some simple quasi-particle description of QCD matter in which
the interaction is modelled phenomenologically by some effective fugacities,
$z$. Embedding such a model in a nonextensive environment allows for a
well-defined separation of the dynamics (represented by $z$) and the
nonextensivity (represented by $q$) and a better understanding of their
relationship.
