Abstract
We broader the view and work out a theory where properties and states are generalized as to have time derivatives of properties and reduced states (density operators) included with compact and flexible ways of calculation. We introduce the notion of entropy as a dispersion measure and consider its time evolution in Markov and quantum processes. We consider limits of stationarity and cross-over between different types of dynamics by taking system environments into account. In each type of dynamics or stationary limit generating functionals appear as the unifying structure. When fields form the configuration space for infinitely many degrees of freedom one deals with stochastic field theories. In the case of quantum processes these are so called quantum field theories met commonly in particle physics and condensed matter physics. Modeling strategies are discussed that start with a Gaussian approximation around stationary action solutions, supplemented with a stability analysis.
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