Mpemba Index and Anomalous Relaxation

The Mpemba effect is a counterintuitive relaxation phenomenon, where a system prepared at a hot temperature cools down faster than an identical system initiated at a cold temperature when both are quenched to an even colder bath. Such nonmonotonic relaxations are observed in various systems, includi...

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Autores principales:	Israel Klich, Oren Raz, Ori Hirschberg, Marija Vucelja
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2019
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b07dd7cc2af84f9691d43967865edbb7
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spelling	oai:doaj.org-article:b07dd7cc2af84f9691d43967865edbb72021-12-02T11:39:51ZMpemba Index and Anomalous Relaxation10.1103/PhysRevX.9.0210602160-3308https://doaj.org/article/b07dd7cc2af84f9691d43967865edbb72019-06-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.9.021060http://doi.org/10.1103/PhysRevX.9.021060https://doaj.org/toc/2160-3308The Mpemba effect is a counterintuitive relaxation phenomenon, where a system prepared at a hot temperature cools down faster than an identical system initiated at a cold temperature when both are quenched to an even colder bath. Such nonmonotonic relaxations are observed in various systems, including water, magnetic alloys, polymers, and driven granular gases. We analyze the Mpemba effect in Markovian dynamics and discover that a stronger version of the effect often exists for a carefully chosen set of initial temperatures. In this strong Mpemba effect, the relaxation time jumps to a smaller value leading to exponentially faster equilibration dynamics. The number of such special initial temperatures defines the Mpemba index, whose parity is a topological property of the system. To demonstrate these concepts, we first analyze the different types of Mpemba relaxations in the mean-field antiferromagnetic Ising model, which demonstrates a surprisingly rich Mpemba-phase diagram. Moreover, we show that the strong effect survives the thermodynamic limit and that it is tightly connected with thermal overshoot; in the relaxation process, the temperature of the relaxing system can decay nonmonotonically as a function of time. Using the parity of the Mpemba index, we then study the occurrence of the strong Mpemba effect in a large class of thermal quench processes and show that it happens with nonzero probability even in the thermodynamic limit. This study is done by introducing the isotropic model for which we obtain analytical lower bound estimates for the probability of the strong Mpemba effects. Consequently, we expect that such exponentially faster relaxations can be observed experimentally in a wide variety of systems.Israel KlichOren RazOri HirschbergMarija VuceljaAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 9, Iss 2, p 021060 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Israel Klich Oren Raz Ori Hirschberg Marija Vucelja Mpemba Index and Anomalous Relaxation
description	The Mpemba effect is a counterintuitive relaxation phenomenon, where a system prepared at a hot temperature cools down faster than an identical system initiated at a cold temperature when both are quenched to an even colder bath. Such nonmonotonic relaxations are observed in various systems, including water, magnetic alloys, polymers, and driven granular gases. We analyze the Mpemba effect in Markovian dynamics and discover that a stronger version of the effect often exists for a carefully chosen set of initial temperatures. In this strong Mpemba effect, the relaxation time jumps to a smaller value leading to exponentially faster equilibration dynamics. The number of such special initial temperatures defines the Mpemba index, whose parity is a topological property of the system. To demonstrate these concepts, we first analyze the different types of Mpemba relaxations in the mean-field antiferromagnetic Ising model, which demonstrates a surprisingly rich Mpemba-phase diagram. Moreover, we show that the strong effect survives the thermodynamic limit and that it is tightly connected with thermal overshoot; in the relaxation process, the temperature of the relaxing system can decay nonmonotonically as a function of time. Using the parity of the Mpemba index, we then study the occurrence of the strong Mpemba effect in a large class of thermal quench processes and show that it happens with nonzero probability even in the thermodynamic limit. This study is done by introducing the isotropic model for which we obtain analytical lower bound estimates for the probability of the strong Mpemba effects. Consequently, we expect that such exponentially faster relaxations can be observed experimentally in a wide variety of systems.
format	article
author	Israel Klich Oren Raz Ori Hirschberg Marija Vucelja
author_facet	Israel Klich Oren Raz Ori Hirschberg Marija Vucelja
author_sort	Israel Klich
title	Mpemba Index and Anomalous Relaxation
title_short	Mpemba Index and Anomalous Relaxation
title_full	Mpemba Index and Anomalous Relaxation
title_fullStr	Mpemba Index and Anomalous Relaxation
title_full_unstemmed	Mpemba Index and Anomalous Relaxation
title_sort	mpemba index and anomalous relaxation
publisher	American Physical Society
publishDate	2019
url	https://doaj.org/article/b07dd7cc2af84f9691d43967865edbb7
work_keys_str_mv	AT israelklich mpembaindexandanomalousrelaxation AT orenraz mpembaindexandanomalousrelaxation AT orihirschberg mpembaindexandanomalousrelaxation AT marijavucelja mpembaindexandanomalousrelaxation
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Mpemba Index and Anomalous Relaxation

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