Superstatistics Based on the Microcanonical Ensemble

with Ei the energy of the microstate labeled by i, β = 1/kBT the inverse temperature (T ), kB Boltzmann’s constant, and ZBG the partition function. The exponential term FBG = exp (−βE) is, of course, called the BG factor. Recently Beck and Cohen [3, 4] have advanced a generalization (called “superstatistics”) of this BG factor, assuming that the inverse temperature β is a stochastic variable. They effect a multiplicative convolution to obtain a generalized statistical factor FGS in the fashion [4]