  Fundamental inconsistencies of superstatistics are highlighted. There is no
such thing as a superposition of Boltzmann factors; what is actually derived is
a generating function and not a normalizable probability density. The beta
density of the second kind for the energy is shown to be subordinated to a
$\chi^2$-probability distribution, and this provides a power-tail distribution
for lage values of the energy, comparable to a Pareto distribution. The
authors' claim that the Laplace method will only work on the inverse Laplace
transform in the opposite limit of small energies is shown to be incorrect. The
exact expression is obtained by contour integration at a multipole located at
the origin corresponding to the high temperature limit.
