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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Autores principales:	Loris Di Cairano, Matteo Gori, Marco Pettini
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	phase transitions differential topology entropy flow Weingarten map Ginzburg-Landau Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/06ad8109ccea43a0850aee98ab9eb293
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id	oai:doaj.org-article:06ad8109ccea43a0850aee98ab9eb293
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spelling	oai:doaj.org-article:06ad8109ccea43a0850aee98ab9eb2932021-11-25T17:29:28ZTopology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions10.3390/e231114141099-4300https://doaj.org/article/06ad8109ccea43a0850aee98ab9eb2932021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1414https://doaj.org/toc/1099-4300Different 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.Loris Di CairanoMatteo GoriMarco PettiniMDPI AGarticlephase transitionsdifferential topologyentropy flowWeingarten mapGinzburg-LandauScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1414, p 1414 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	phase transitions differential topology entropy flow Weingarten map Ginzburg-Landau Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	phase transitions differential topology entropy flow Weingarten map Ginzburg-Landau Science Q Astrophysics QB460-466 Physics QC1-999 Loris Di Cairano Matteo Gori Marco Pettini Topology and Phase Transitions: A First Analytical Step towards the Definition of Sufficient Conditions
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.
format	article
author	Loris Di Cairano Matteo Gori Marco Pettini
author_facet	Loris Di Cairano Matteo Gori Marco Pettini
author_sort	Loris Di Cairano
title	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_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_sort	topology and phase transitions: a first analytical step towards the definition of sufficient conditions
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/06ad8109ccea43a0850aee98ab9eb293
work_keys_str_mv	AT lorisdicairano topologyandphasetransitionsafirstanalyticalsteptowardsthedefinitionofsufficientconditions AT matteogori topologyandphasetransitionsafirstanalyticalsteptowardsthedefinitionofsufficientconditions AT marcopettini topologyandphasetransitionsafirstanalyticalsteptowardsthedefinitionofsufficientconditions
_version_	1718412266409295872

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

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