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Santos A. Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law. Phys Rev E 2024; 109:044149. [PMID: 38755857 DOI: 10.1103/physreve.109.044149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2024] [Accepted: 04/01/2024] [Indexed: 05/18/2024]
Abstract
Despite extensive research, the fundamental physical mechanisms underlying the Mpemba effect, a phenomenon where a substance cools faster after initially being heated, remain elusive. Although historically linked with water, the Mpemba effect manifests across diverse systems, sparking heightened interest in Mpemba-like phenomena. Concurrently, the Kovacs effect, a memory phenomenon observed in materials such as polymers, involves rapid quenching and subsequent temperature changes, resulting in nonmonotonic relaxation behavior. This paper probes the intricacies of the Mpemba and Kovacs effects within the framework of the time-delayed Newton's law of cooling, recognized as a simplistic yet effective phenomenological model accommodating memory phenomena. This law allows for a nuanced comprehension of temperature variations, introducing a delay time (τ) and incorporating specific protocols for the thermal bath temperature, contingent on a defined waiting time (t_{w}). Remarkably, the relevant parameter space is two-dimensional (τ and t_{w}), with bath temperatures exerting no influence on the presence or absence of the Mpemba effect or on the relative strength of the Kovacs effect. The findings enhance our understanding of these memory phenomena, providing valuable insights applicable to researchers across diverse fields, ranging from physics to materials science.
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Affiliation(s)
- Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
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2
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Pemartín IGA, Mompó E, Lasanta A, Martín-Mayor V, Salas J. Shortcuts of Freely Relaxing Systems Using Equilibrium Physical Observables. PHYSICAL REVIEW LETTERS 2024; 132:117102. [PMID: 38563945 DOI: 10.1103/physrevlett.132.117102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 11/15/2023] [Accepted: 01/18/2024] [Indexed: 04/04/2024]
Abstract
Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to shorten the time needed to cool down (or heat up) a system. Though, a strategy to design these effects in mesoscopic systems is missing. We bring forward a description that allows us to formulate such strategies, and, along the way, makes natural these paradoxical behaviors. In particular, we study the evolution of macroscopic physical observables of systems freely relaxing under the influence of one or two instantaneous thermal quenches. The two crucial ingredients in our approach are timescale separation and a nonmonotonic temperature evolution of an important state function. We argue that both are generic features near a first-order transition. Our theory is exemplified with the one-dimensional Ising model in a magnetic field using analytic results and numerical experiments.
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Affiliation(s)
| | - Emanuel Mompó
- Departamento de Matemática Aplicada, Grupo de Dinámica No Lineal, Universidad Pontificia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain
- Instituto de Investigación Tecnológica (IIT), Universidad Pontificia Comillas, 28015 Madrid, Spain
| | - Antonio Lasanta
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, Cortadura del Valle, s/n, 51001 Ceuta, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
- Nanoparticles Trapping Laboratory, Universidad de Granada, Granada, Spain
| | - Víctor Martín-Mayor
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
| | - Jesús Salas
- Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Spain
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Chatterjee AK, Takada S, Hayakawa H. Quantum Mpemba Effect in a Quantum Dot with Reservoirs. PHYSICAL REVIEW LETTERS 2023; 131:080402. [PMID: 37683159 DOI: 10.1103/physrevlett.131.080402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 07/17/2023] [Indexed: 09/10/2023]
Abstract
We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold) cross each other at finite time (and thereby reverse their identities; i.e., hot becomes cold and vice versa) to generate thermal quantum Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.
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Affiliation(s)
- Amit Kumar Chatterjee
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Satoshi Takada
- Department of Mechanical Systems Engineering and Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
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Biswas A, Rajesh R. Mpemba effect for a Brownian particle trapped in a single well potential. Phys Rev E 2023; 108:024131. [PMID: 37723739 DOI: 10.1103/physreve.108.024131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 08/03/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect refers to the counterintuitive phenomenon of a hotter system equilibrating faster than a colder system when both are quenched to the same low temperature. For a Brownian particle trapped in a piecewise linear single well potential that is devoid of any other metastable minima, we show the existence of the Mpemba effect for a wide range of parameters through an exact solution. This result challenges the prevalent explanation of the Mpemba effect that requires the energy landscape to be rugged with multiple minima. We also demonstrate the existence of inverse and strong Mpemba effects.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Biswas A, Prasad VV, Rajesh R. Mpemba effect in driven granular gases: Role of distance measures. Phys Rev E 2023; 108:024902. [PMID: 37723801 DOI: 10.1103/physreve.108.024902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 07/25/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect refers to the counterintuitive effect where a system which is initially further from the final steady state equilibrates faster than an identical system that is initially closer. The closeness to the final state is defined in terms of a distance measure. For driven granular systems, the Mpemba effect has been illustrated in terms of an ad hoc measure of mean kinetic energy as the distance function. In this paper, by studying four different distance measures based on the mean kinetic energies as well as velocity distribution, we show that the Mpemba effect depends on the definition of the measures.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - V V Prasad
- Department of Physics, Cochin University of Science and Technology, Kochi 682022, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Amorim F, Wisely J, Buckley N, DiNardo C, Sadasivan D. Predicting the Mpemba effect using machine learning. Phys Rev E 2023; 108:024137. [PMID: 37723698 DOI: 10.1103/physreve.108.024137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Accepted: 08/01/2023] [Indexed: 09/20/2023]
Abstract
The Mpemba effect can be studied with Markovian dynamics in a nonequilibrium thermodynamics framework. The Markovian Mpemba effect can be observed in a variety of systems including the Ising model. We demonstrate that the Markovian Mpemba effect can be predicted in the Ising model with several machine learning methods: the decision tree algorithm, neural networks, linear regression, and nonlinear regression with the least absolute shrinkage and selection operator (LASSO) method. The positive and negative accuracy of these methods are compared. Additionally, we find that machine learning methods can be used to accurately extrapolate to data outside the range in which they were trained. Neural networks can even predict the existence of the Mpemba effect when they are trained only on data in which the Mpemba effect does not occur. This indicates that information about which coefficients result in the Mpemba effect is contained in coefficients where the results does not occur. Furthermore, neural networks can predict that the Mpemba effect does not occur for positive J, corresponding to the ferromagnetic Ising model even when they are only trained on negative J, corresponding to the antiferromagnetic Ising model. All of these results demonstrate that the Mpemba effect can be predicted in complex, computationally expensive systems, without explicit calculations of the eigenvectors.
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Affiliation(s)
| | - Joey Wisely
- Ave Maria University, Ave Maria, Florida 34142, USA
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Biswas A, Rajesh R, Pal A. Mpemba effect in a Langevin system: Population statistics, metastability, and other exact results. J Chem Phys 2023; 159:044120. [PMID: 37522403 DOI: 10.1063/5.0155855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 07/06/2023] [Indexed: 08/01/2023] Open
Abstract
The Mpemba effect is a fingerprint of the anomalous relaxation phenomenon wherein an initially hotter system equilibrates faster than an initially colder system when both are quenched to the same low temperature. Experiments on a single colloidal particle trapped in a carefully shaped double well potential have demonstrated this effect recently [A. Kumar and J. Bechhoefer, Nature 584, 64 (2020)]. In a similar vein, here, we consider a piece-wise linear double well potential that allows us to demonstrate the Mpemba effect using an exact analysis based on the spectral decomposition of the corresponding Fokker-Planck equation. We elucidate the role of the metastable states in the energy landscape as well as the initial population statistics of the particles in showcasing the Mpemba effect. Crucially, our findings indicate that neither the metastability nor the asymmetry in the potential is a necessary or a sufficient condition for the Mpemba effect to be observed.
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Affiliation(s)
- Apurba Biswas
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Arnab Pal
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Das SK. Perspectives on a Few Puzzles in Phase Transformations: When Should the Farthest Reach the Earliest? LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023. [PMID: 37499235 DOI: 10.1021/acs.langmuir.3c00668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
We briefly review the facts concerning two important aspects of phase transitions, namely, critical and coarsening phenomena. A discussion of the universal features, highlighting the current challenges, is provided. Following this, we elaborate on a topic of much recent interest, viz., the Mpemba effect, a puzzle that found mention even in the works of Aristotle. After a description of the debated case of faster freezing of a hotter sample of liquid water, into ice, than a colder one, when quenched to the same subzero temperature, we discuss more modern interest. There one asks, should a hotter body of a material equilibrate faster than a colder one when quenched to a common lower temperature? Within this broad scenario, we focus on magnetic systems. A surprising observation of the effect during the para- to ferromagnetic transition, in a simple model system, viz., the nearest-neighbor Ising model, without any built-in frustration, is described. Some associated future directions are pointed out. A discussion is provided by considering the effect as a kinetic outcome in the background of critical phenomena. A picture is drawn by putting emphasis on the role of spatial correlations in the initial configurations alongside discussing the importance of frustration and metastability in evolution from one state to another. In connection with dynamical freezing, concerning metastability, we have introduced the complex Ginzburg-Landau equation that has relevance in phase transitions, chemical oscillations, and elsewhere. For this model and a few other cases also, we have described how a lack of order or correlation in certain parameters can lead to quicker evolution.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Teza G, Yaacoby R, Raz O. Relaxation Shortcuts through Boundary Coupling. PHYSICAL REVIEW LETTERS 2023; 131:017101. [PMID: 37478423 DOI: 10.1103/physrevlett.131.017101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Revised: 07/06/2022] [Accepted: 05/17/2023] [Indexed: 07/23/2023]
Abstract
When a hot system cools down faster than an equivalent cold one, it exhibits the Mpemba effect (ME). This counterintuitive phenomenon was observed in several systems including water, magnetic alloys, and polymers. In most experiments the system is coupled to the bath through its boundaries, but all theories so far assumed bulk coupling. Here we build a general framework to characterize anomalous relaxations through boundary coupling, and present two emblematic setups: a diffusing particle and an Ising antiferromagnet. In the latter, we show that the ME can survive even arbitrarily weak couplings.
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Affiliation(s)
- Gianluca Teza
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ran Yaacoby
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Oren Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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Megías A, Santos A, Prados A. Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag. Phys Rev E 2022; 105:054140. [PMID: 35706208 DOI: 10.1103/physreve.105.054140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equation and event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the crossing of the evolution curves of the kinetic temperature (average kinetic energy), and, second, the stochastic thermodynamics or entropic route, in which the Mpemba effect is characterized by the crossing of the distance to equilibrium in probability space. In general, a nonmutual correspondence between the thermal and entropic Mpemba effects is found, i.e., there may appear the thermal effect without its entropic counterpart or vice versa. Furthermore, a nontrivial overshoot with respect to equilibrium of the thermal relaxation makes it necessary to revise the usual definition of the thermal Mpemba effect, which is shown to be better described in terms of the relaxation of the local equilibrium distribution. Our theoretical framework, which involves an extended Sonine approximation in which not only the excess kurtosis but also the sixth cumulant is retained, gives an excellent account of the behavior observed in simulations.
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Affiliation(s)
- Alberto Megías
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Andrés Santos
- Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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