Mpemba effect of a mean-field system: The phase transition time

Mpemba effect in pure spin systems : A universal picture of the role of spatial correlations at initial states

The quicker freezing of hotter water, than a colder sample, when quenched to a common lower temperature, is referred to as the Mpemba effect (ME). While this counter-intuitive fact remains a surprize since long, efforts have begun to identify similar effect in other systems. We investigate the ME in a rather general context concerning magnetic phase transitions. From Monte Carlo simulations of model systems, viz., the Ising model and the q-state Potts model, with varying range of interaction and space dimension, we assert that hotter paramagnets undergo ferromagnetic ordering faster than the colder ones. This conclusion we have arrived at following the analyses of the simulation results on decay of energy and growth in ordering following quenches from different starting temperatures, to fixed final temperatures below the Curie points. The general observation, in all the considered models, without any element of frustration, is a crucial and important fact of our study. Furthermore, we have obtained an important scaling picture, on the strength of the effect, with respect to the variation in spatial correlation in the initial states. This behavior appears true irrespective of the nature of order-parameter fluctuation and even order of transition. The observations are expected to be relevant to the understanding of ME in a rather general class of systems.

Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law

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.

Quantum Mpemba Effect in a Quantum Dot with Reservoirs

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.

Perspectives on a Few Puzzles in Phase Transformations: When Should the Farthest Reach the Earliest?

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.

Relaxation Shortcuts through Boundary Coupling

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.

The Curious Case of 1-Ethylpyridinium Triflate: Ionic Liquid Exhibiting the Mpemba Effect

Here, we report the results of qualitative and quantitative investigations of the first-order phase transition in the ionic liquid 1-ethylpyridinium triflate exhibiting a high variability of temperature ranges, within which the freezing and melting occur. By two methods, the direct fast quenching/annealing and the slow temperature-controlled differential scanning calorimeter, it is revealed that despite the almost constant absolute enthalpies of phase transition, the freezing occurs faster with the larger temperature contrast (cooling rate) between the initially hotter sample and the colder surrounding. This feature is a clear exhibition of the Mpemba effect. The regularity in the change of the melting point is analyzed as well.

Theoretical model for the Mpemba effect through the canonical first-order phase transition

The Mpemba effect is the phenomenon in which the system with high initial temperature cools faster than the system with low initial temperature when all other conditions are the same. A theoretical model of the Mpemba effect through the canonical first-order phase transition is proposed in this paper, which shows that in the cooling processes, the path of the first-order phase transition of the system with the high initial temperature does not pass through any metastable state, while the path of the first-order phase transition of the system with the low initial temperature passes through a metastable state, which leads to the occurrence of the Mpemba effect. Then an example of the theoretical model is given in the Blume-Emery-Griffiths model. The Monte Carlo algorithm is adopted to calculate the estimated times for both systems with different initial temperature to cool down and undergo a first-order phase transition. The simulation results demonstrate a Mpemba effect in the system. Moreover, the evolution paths of the first-order phase transitions of the systems with high and low initial temperatures are given, respectively. The theoretical model presented here may help explain the Mpemba effect in water.

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag

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.