The structure of high-frequency time series of financial data taking the DAX future as an example is investigated with respect to the existence of local order on a time horizon of a few minutes. We will show that there might be special local situations where local order exists and where the...

This work is devoted to applications of the Ehrenfest urn model to innovation and search processes. In the first part we discuss systems of two urns serving as models of innovation processes. The elementary act of innovation is considered as a transition from old (technologies, way of...

The quantum statistics of electrons interacting with nonlinear excitations of a classical heated nonlinear lattice of atoms is studied. By using tight-binding approximation, Wigner momentum distributions and computer simulations we show the existence of quite fast and nearly loss-free motions of...

A model of Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion, is discussed. The general dynamics outlined in Section 2, is investigated for the deterministic and stochastic...

A stochastic theory is presented for nucleation and growth of clusters in a finite system. We consider a discrete cluster distribution for which the free energy and the equilibrium probability distribution are derived. The cluster growth and shrinkage occurs by the attachment/evaporation of free...

The valoric interpretation developed already by Clausius, Helmholtz and Ostwald is taken as the basis for a reinterpretation of the various entropy concepts developed by Clausius, Boltzmann, Gibbs, Shannon and Kolmogorov. As the key points we consider the value of energy with respect to work and...

Unidirectional solitonic wave-mediated transport is shown to be possible for a class of anharmonic lattice problems where, due to wave asymmetry, the waves can be used as a traveling periodic ratchet. Using a (mesoscopic) probabilistic description we have assessed the role of both viscous...

We consider here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion. New solutions for the stationary distribution of swarms with linear attraction are given in mean field approximation....

By using the available knowledge about the thermodynamic functions for the low-temperature Wigner region (lattice formulae and Gell-Mann-Brueckner formulae) as well as for the high-temperature Debye region (limiting law with quantum corrections) Pade approximations are constructed. The formulae...

The mean uncertainties of probability distributions of discrete sets of events and those of dynamic sequences of events are investigated on the macroscopic and on the microscopic level. First one-time distributions are studied. The key point is the specification of the state space; the...