A general microscopic and macroscopic theory is developed for systems which are governed by a {linear) master equation. The theory is based on a network representation of the master equation, and the results are obtained mostly by application of some basic theorems of mathematical graph theory. In the microscopic part of the theory, the construction of a steady state solution of the master equation in terms of graph theoretical elements is, described (KirchhofFs theorem), and it is shown that the master equation satisfies a global asymptotic Liapunov stability criterion with respect to this state. The Cxlansdorff -Prigogine criterion turns out to be the differential version and thus a special case of the global criterion. In the macroscopic part of the theory, a general prescription is given describing macrostates of the systems arbitrarily fear from equilibrium in the language of generalized forces and fluxes of nonlinear irreversible thermodynamics.As a particular result, Onsager s reciprocity relations for the phenomenological coefficients are obtained as coinciding with the reciprocity relations of a near-toequilibrium network.

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Impurity hopping conduction in polar lattices and amorphous substances is investigated by application of the canonical transformation of the small polaron theory. In the case of acoustic coupling only, the results of Miller and Abrahams and Gosar for one-phonon processes are recovered and compared with the contributions of multi-phonon processes. I n the polar case the assisting roles of acoustic and polar phonons are discussed seperately a t temperatures T > 012 and T < 612 ( 6 being the Debye temperature). The type of the temperature dependence of the conductivity is determined.Es wird die Storstellen-Hoppingleitfahigkeit in polaren Gittern und amorphen Substanzen mit der Anwendung der kanonischen Transformation aus der Theorie des kleinen Polarons untersucht. I m Falle der rein akustischen Kopplung werden die Ergebnisse von Miller und Abrahams und von Gosar fur Ein-Phonon-Prozesse verifiziert und mit den Beitragen von Mehr-Phononen-Prozessen verglichen. I m Fall des polaren Gitters wird die assistierende Rolle der akustischen und polaren Phononen getrennt fur die Temperaturen T > 012 und T < 012 ( 6 Debye Temperatur) diskutiert. Die Temperaturabhangigkeit der LeitfSihigkeit wird bestimmt.

Multistability in vision is an intriguing phenomenon that is currently not well understood. In this paper, we present a new, stochastic model for multistable visual perception. It is based on results of time series analysis of experimental data, yielding evidence for it being a linear, stochastic process. This is the outcome of testing for unstable periodic orbits and comparing the correlation dimension of the data to that of white noise. In the model, all degrees of freedom but one can be determined by general knowledge, thus resulting in a high degree of parsimony. The remaining parameter is used to model the individual characteristics that vary between subjects. Fitting simulations to the experimental data proves the parameter to be in a physiologically highly plausible range.