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Information Macrodynamics (IMD) belong to an interdisciplinary science that represents a new theoretical and computer-based methodology for a system informational descriptionand improvement,including various activities in such areas as thinking, intelligent processes, communications, management, and other nonphysical subjects with their mutual interactions, informational superimposition, and theinformation transferredbetweeninteractions. The IMD is based on the implementation of a single concept by a unique mathematical principle and formalism, rather than on an artificial combination of many arbitrary, auxiliary concepts and/or postulates and different mathematical subjects, such as the game, automata, catastrophe, logical operations theories, etc. This concept is explored mathematically using classical mathematics as calculus of variation and the probability theory, which are potent enough, without needing to developnew,specifiedmathematical systemicmethods. The formal IMD model automatically includes the related results from other fields, such as linear, nonlinear, collective and chaotic dynamics, stability theory, theory of information, physical analogies of classical and quantum mechanics, irreversible thermodynamics, andkinetics. The main IMD goal is to reveal the information regularities, mathematically expressed by the considered variation principle (VP), as a mathematical tool to extractthe regularities and define the model, whichdescribes theregularities. The IMD regularities and mechanisms are the results of the analytical solutions and are not retained by logical argumentation, rational introduction, and a reasonable discussion. The IMD's information computer modeling formalism includes a human being (as an observer, carrier and producer ofinformation), with a restoration of the model during the objectobservations.



I. The IMD Essence and Concepts

Let us define an elementary event as a something that may occur or may not occur. Such an elementary event automatically carries a measure of its existence or a certainty.
Vladimir S. Lerner

II. Mathematical Foundations of Informational Macrodynamics

Mode of microlevel process.
Vladimir S. Lerner

III. Applications

Let us consider the problem of restoration of operator of the random process that is defined by the differential equation of a homogenous system:
$$ \frac{{dx}}{{dt}} = Ax + \tilde{g},A = \left( {t',x} \right) $$
where \(\tilde{g} \) is a known function of time, depending on initial conditions of the state vector x=x(0), with its probability density function p=p(x(0)). The above equation can be obtained, for example, by averaging a stochastic differential equation.
Vladimir S. Lerner


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