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
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Lenguaje:EN
Publicado: MDPI AG 2021
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Acceso en línea:https://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
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