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The von Neumann Entropy for Mixed States
The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entr...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514141/ https://www.ncbi.nlm.nih.gov/pubmed/33266765 http://dx.doi.org/10.3390/e21010049 |
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author | Anaya-Contreras, Jorge A. Moya-Cessa, Héctor M. Zúñiga-Segundo, Arturo |
author_facet | Anaya-Contreras, Jorge A. Moya-Cessa, Héctor M. Zúñiga-Segundo, Arturo |
author_sort | Anaya-Contreras, Jorge A. |
collection | PubMed |
description | The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki–Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction. |
format | Online Article Text |
id | pubmed-7514141 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75141412020-11-09 The von Neumann Entropy for Mixed States Anaya-Contreras, Jorge A. Moya-Cessa, Héctor M. Zúñiga-Segundo, Arturo Entropy (Basel) Article The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki–Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction. MDPI 2019-01-10 /pmc/articles/PMC7514141/ /pubmed/33266765 http://dx.doi.org/10.3390/e21010049 Text en © 2019 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Anaya-Contreras, Jorge A. Moya-Cessa, Héctor M. Zúñiga-Segundo, Arturo The von Neumann Entropy for Mixed States |
title | The von Neumann Entropy for Mixed States |
title_full | The von Neumann Entropy for Mixed States |
title_fullStr | The von Neumann Entropy for Mixed States |
title_full_unstemmed | The von Neumann Entropy for Mixed States |
title_short | The von Neumann Entropy for Mixed States |
title_sort | von neumann entropy for mixed states |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514141/ https://www.ncbi.nlm.nih.gov/pubmed/33266765 http://dx.doi.org/10.3390/e21010049 |
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