  Quasi-power law ensembles are discussed from the perspective of nonextensive
Tsallis distributions characterized by a nonextensive parameter $q$. A number
of possible sources of such distributions are presented in more detail. It is
further demonstrated that data suggest that nonextensive parameters deduced
from Tsallis distributions functions $f\left(p_T\right)$, $q_1$, and from
multiplicity distributions (connected with Tsallis entropy), $q_2$, are not
identical and that they are connected via $q_1 + q_2 = 2$. It is also shown
that Tsallis distributions can be obtained directly from Shannon information
entropy, provided some special constraints are imposed. They are connected with
the type of dynamical processes under consideration (additive or
multiplicative). Finally, it is shown how a Tsallis distribution can
accommodate the log-oscillating behavior apparently seen in some multiparticle
data.
