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Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions

Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that...

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Detalles Bibliográficos
Autores principales: Di Cairano, Loris, Gori, Matteo, Pettini, Marco
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8621195/
https://www.ncbi.nlm.nih.gov/pubmed/34828112
http://dx.doi.org/10.3390/e23111414
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author Di Cairano, Loris
Gori, Matteo
Pettini, Marco
author_facet Di Cairano, Loris
Gori, Matteo
Pettini, Marco
author_sort Di Cairano, Loris
collection PubMed
description Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy.
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spelling pubmed-86211952021-11-27 Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions Di Cairano, Loris Gori, Matteo Pettini, Marco Entropy (Basel) Article Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy. MDPI 2021-10-27 /pmc/articles/PMC8621195/ /pubmed/34828112 http://dx.doi.org/10.3390/e23111414 Text en © 2021 by the authors. 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
Di Cairano, Loris
Gori, Matteo
Pettini, Marco
Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
title Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
title_full Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
title_fullStr Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
title_full_unstemmed Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
title_short Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
title_sort topology and phase transitions: a first analytical step towards the definition of sufficient conditions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8621195/
https://www.ncbi.nlm.nih.gov/pubmed/34828112
http://dx.doi.org/10.3390/e23111414
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