Fundamental inconsistencies of 'superstatistics'

Abstract

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 $χ^2$-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.