Correlations in superstatistical systems

We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental data. Excellent agreement is obtained for various measured quantities, such as acceleration probability densities, Lagrangian scaling exponents, correlations between acceleration components, and time decay of correlations. We comment on how to proceed from superstatistics to a thermodynamic description.