Superstatistics: Theory and Applications

Abstract:

Many driven nonequilibrium systems are described by a superposition of several dynamics on various time scales. If time scales are clearly separated then the formalism of superstatistics can be applied, leading effectively to a more general statistical mechanics relevant for complex systems. In these types of systems there is often dynamical behavior that is characterized by spatio-temporal fluctuations of an intensive parameter $\beta$. This parameter may be for example the inverse temperature, or an effective friction constant, or the amplitude of Gaussian white noise, or the energy dissipation in turbulent flows, or simply a local variance parameter extracted from a measured signal. A nonhomogenoeus spatially extended system with fluctuations in $\beta$ on a large time scale, larger than the local relaxation time, leads to a superstatistical description, by averaging local Boltzmann factors using a suitable weight function $f(\beta)$. Kappa distributions in space plasma physics are one example which naturally follows out of this formalism, but there are many applications in other areas as well. In this talk I will sketch the basic theory underlying the superstatistical approach and then describe a couple of recent applications.