Superstatistics is a branch of statistical mechanics or statistical physics devoted to the study of non-linear and non-equilibrium systems. It is characterized by using the superposition of multiple differing statistical models to achieve the desired non-linearity. In terms of ordinary statistical ideas, this is equivalent to compounding the distributions of random variables and it may be considered a simple case of a doubly stochastic model.
Consider an extended thermodynamical system which is locally in equilibrium and has a Boltzmann distribution, that is the probability of finding the system in a state with energy
This defines the superstatistical partition function
where the system can assume discrete energy states
Modeling the fluctuations of