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 E is proportional to exp ⁡ ⁡ ( − − β β E ) . Here β β is the local inverse temperature. A non-equilibrium thermodynamical system is modeled by considering macroscopic fluctuations of the local inverse temperature. These fluctuations happen on time scales which are much larger than the microscopic relaxation times to the Boltzmann distribution. If the fluctuations of β β are characterized by a distribution f ( β β ) , the superstatistical Boltzmann factor of the system is given by