| Authors |
Vladimir K. Fedorov, Doctor of technical sciences, professor, professor of sub-department of power supply, of industrial enterprises, Omsk State Technical University (11 Mira avenue, Omsk, Russia) pestrikova_omgt@inbox.ru
Irina E. Pestrikova, Postgraduate student, Omsk State Technical University (11 Mira avenue, Omsk, Russia) pestrikova_omgt@inbox.ru
Igor V. Fedorov, Candidate of technical sciences, associate professor of sub-department of applied mathematics and fundamental computer science, Omsk State Technical University (11 Mira avenue, Omsk, Russia) pestrikova_omgt@inbox.ru
Ekaterina V. Anoshenkova, Senior lecturer, sub-department of theoretical and general electrical engineering, Omsk State Technical University (11 Mira avenue, Omsk, Russia) pestrikova_omgt@inbox.ru
Dmitry V. Fedorov, Candidate of technical sciences, chief specialist (power engineer), Gazpromneft-ONPZ JSC (1 Gubkin avenue, Omsk, Russia) pestrikova_omgt@inbox.ru
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| Abstract |
Background. One of the important scientific problems of the theory of the electrical system topic is the solution of the problem of predicting the behavior of the studied indicators of electricity quality in time and phase space based on certain knowledge about the initial state of EFV. This task is reduced to finding some law that allows, according to available information about EFV at a partial time t0 at the point x0 of the phase space, to determine its future at any time t > t0.
Materials and methods. The mathematical model of the electrical system is a co-deterministic system of nonlinear differential equations with given initial conditions, the solution of which behaves unpredictably and randomly – this type of solution is called the mode of deterministic chaos and this is a new type and a special form of ETS behavior. In this work, entropy and its maximization are considered in connection with various possible trajectories of the movement of a chaotic system in the phase space between two points (cells). Macsimilation of entropy leads to a distribution of the probability of choosing a trajectory as a function of action, from which the probability of a transition of an electrical system from one state to another state can be easily obtained.
Results. An interesting result of the study is that the most believable trajectories are simply the paths of least action. This suggests that the principle of least action in a probabilistic situation is equivalent to the principle of maximizing entropy or uncertainty associated with a particular probability distribution.
Output. The conclusion of the study is that, most likely, motion paths are the least action paths. Thus, in a probabilistic situation, the principle of least action is equivalent to the principle of maximizing entropy or uncertainty, which is associated with a diverse probability distribution.
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| Key words |
entropy, entropy instability, entropy maximization principle, least action principle, motion trajectories, least action paths, probability distribution, nonlinear equation, non-equilibrium system, phase space, bifurcation point, fluctuations, iteration, local positive feedback, electrical system
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