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Algebraical Entropy and Arrow of Time
Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical results of a measurement, which requires at least three ingredien...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689210/ https://www.ncbi.nlm.nih.gov/pubmed/36359614 http://dx.doi.org/10.3390/e24111522 |
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author | Gogberashvili, Merab |
author_facet | Gogberashvili, Merab |
author_sort | Gogberashvili, Merab |
collection | PubMed |
description | Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical results of a measurement, which requires at least three ingredients: object, device and observer, in the non-associative case depends on ordering of operations and is ambiguous. We show that use of octonions as a fundamental algebra, in any measurement, leads to generation of unavoidable 18.6 bit relative entropy of the probability density functions of the active and passive transformations, which correspond to the groups G2 and SO(7), respectively. This algebraical entropy can be used to determine the arrow of time, analogically as thermodynamic entropy does. |
format | Online Article Text |
id | pubmed-9689210 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-96892102022-11-25 Algebraical Entropy and Arrow of Time Gogberashvili, Merab Entropy (Basel) Article Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical results of a measurement, which requires at least three ingredients: object, device and observer, in the non-associative case depends on ordering of operations and is ambiguous. We show that use of octonions as a fundamental algebra, in any measurement, leads to generation of unavoidable 18.6 bit relative entropy of the probability density functions of the active and passive transformations, which correspond to the groups G2 and SO(7), respectively. This algebraical entropy can be used to determine the arrow of time, analogically as thermodynamic entropy does. MDPI 2022-10-25 /pmc/articles/PMC9689210/ /pubmed/36359614 http://dx.doi.org/10.3390/e24111522 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Gogberashvili, Merab Algebraical Entropy and Arrow of Time |
title | Algebraical Entropy and Arrow of Time |
title_full | Algebraical Entropy and Arrow of Time |
title_fullStr | Algebraical Entropy and Arrow of Time |
title_full_unstemmed | Algebraical Entropy and Arrow of Time |
title_short | Algebraical Entropy and Arrow of Time |
title_sort | algebraical entropy and arrow of time |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689210/ https://www.ncbi.nlm.nih.gov/pubmed/36359614 http://dx.doi.org/10.3390/e24111522 |
work_keys_str_mv | AT gogberashvilimerab algebraicalentropyandarrowoftime |