Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On "classical" and "quantum" Limits at the Integration of a System of Autonomous Differential Equations

Author(s):

Olga Nikolaevna Khatuntseva

Doctor of Physical and Mathematical Sciences,
academic secretary Rocket Space Corporation “Energia” named after S.P.Korolev,
Professor of the Department of Aerophysical Mechanics and Motion Control
Federal State Autonomous Educational Institution of Higher Education "Moscow Institute of Physics and Technology (State University)"

ol-khatun@yandex.ru

Abstract:

The studies carried out in the author's earlier works show the possibility of a stochastic process in the numerical integration of systems of autonomous differential equations (ADE) of the Lorentz type. They also noted that with an increase in the number of equations (degrees of freedom) in the ADE system, the stochastic nature of the process decreases – the "determinization" of the process occurs. In this paper, an attempt is made to characterize the process of transition from one iterative step to another (when integrating the ADE system by numerical methods) by some average value of the time interval for all the equations of the system, and then to determine the relationship between this value and the change in the entropy of the system. Two limiting cases are found when describing such a system: "classical" - when time monotonically increases during the transition from one iterative step to another, and "quantum" - when time is defined ambiguously and a violation of cause-and-effect relationships in the system is possible.

Keywords

References:

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