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...
Guardado en:
Autores principales: | , , |
---|---|
Formato: | article |
Lenguaje: | EN |
Publicado: |
MDPI AG
2021
|
Materias: | |
Acceso en línea: | https://doaj.org/article/06ad8109ccea43a0850aee98ab9eb293 |
Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
id |
oai:doaj.org-article:06ad8109ccea43a0850aee98ab9eb293 |
---|---|
record_format |
dspace |
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 |