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This book is based on my research work I did between 1986 and 1992 at the Institut fur Theoretische Physik und Synergetik, Universitiit Stuttgart. It might be of interest to all students and scientists who are interested in modern mathematical physics. It deals with one of the essential topics of modern physical research, namely t. he problem of universal aspects in statistical physics, and in doing so multi-component systems, like thermodynamic systems, laser systems and high-dimensional quan tum systems, are considered. Synergetic aspects of multi-component systems will be discussed. Remarks to biological systems will be made, in particular remarks to the problem of EEG analysis. Non-linear aspects will be discussed. The problem of a macroscopic access to multi-component systems was an essential part of my research work. In this context it has to be emphasized that in this book the concept of hyper-surface equations will be introduced, which is a totally analytical strategy to determine distribution function parameters in an exact way by using only given measurement quantities. This concept can be used to determine both distribution functions of macroscopic systems and path integrals of quantum systems. In this context the property self-similarity will playa crucial role. A special extreme princi ple, the maximum information entropy principle, can be taken as a basis to introduce this concept. This principle will be discussed. In order to determine the dynamic behavior of multi-component systems, special evolution equations are needed.
