Superstatistical fluctuations in time series: applications to share-price dynamics and turbulence.

We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter beta that fluctuates on a large time scale as compared to the other time scales of the complex system under consideration. The proposed method extracts the main superstatistical parameters out of a given data set and examines the validity of the superstatistical model assumptions.

Superstatistical distributions from a maximum entropy principle.

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: the superstatistical quantum-mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.

Transition records of stationary Markov chains.

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed.

Urine analysis of European moles Talpa europaea and white rats Rattus norvegicus kept on a carnivore's diet.

1. The urine compositions of the European mole Talpa europaea and of the white rat Rattus norvegicus (albino) kept on a carnivore's diet were compared. 2.