System Analysis

Abstract

The statistical behavior of many classes of physical systems is governed by exponential distribution functions of a special order. Some examples are given in table 4.1. As the reader can see, thermodynamic distribution functions as well as distribution functions of the statistical laser theory are exponential distribution functions of a special order. In order to describe quantum systems, it is possible to use special path integrals, namely Feynman path integrals. Path integrals, too, can be incorporated into these considerations, as such integrals contain exponential functions as central parts. It has to be mentioned here that in the same way path integrals which occur in the theory of Fokker-Planck equations can be incorporated. As many functions can be described in a more or less approximative way by a Taylor expansion, many non-exponential functions can be incorporated in these considerations, too. Furthermore, it has to be mentioned here that functions usable in an approximative brain research are sometimes exponential distribution functions of a special order. All these functions can then be described by only one mathematical expression, in which case a special physical system is given by a special choice of the distribution function parameters. In particular, thermodynamic distribution function parameters are functions of the absolute temperature, specific laser distribution function parameters are functions of the inversion, of loss constants, etc., and distribution functions of brain theory may show dependences of the environmental activity, i. e. of the outer scene.