title: On "classical" and "quantum" Limits at the Integration of a System of Autonomous Differential Equations
metadata.name: dc.contributor.author
metadata.value: Khatuntseva, Olga Nikolaevna
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-12-02T12:57:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-12-02T12:57:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-03
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2024.104
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/48039
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Differential Equations and Control Processes;Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: time
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: chaos
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: autonomous differential equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lorentz system of equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stochastic processes
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quantum systems
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On "classical" and "quantum" Limits at the Integration of a System of Autonomous Differential Equations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 24104-jdecp-khatuntseva.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/48039/1/24104-jdecp-khatuntseva.pdf
resources.format: Adobe PDF
resources.size: 672,82 kB