Inducing and optimizing Markovian Mpemba effect with stochastic reset

Busiello, Daniel Maria; Gupta, Deepak; Maritan, Amos

doi:10.1088/1367-2630/ac2922

Cited by 32 publications

(22 citation statements)

References 56 publications

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“…In recent years the term "Mpemba effect" was extended, and it is now used to describe a wide range of non-monotonic relaxation phenomena. These include experimental observations of hot systems that undergo a phase transition before cold systems in non-water substances (Polymers [10], Clathrate hydrates [11]), as well as in other types of phase transitions (Magnetic transition in alloys [12] and various spin models [13][14][15][16][17]), relaxation towards equilibrium without a phase transition that is non-monotonous in the initial temperature [18][19][20][21][22] and similar effects in relaxation towards a nonequilibrium steady states in driven molecular gas models [23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Landau Theory for the Mpemba Effect Through Phase Transitions

Holtzman¹,

Raz²

2022

Preprint

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The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.

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Section: Introductionmentioning

confidence: 99%

Landau Theory for the Mpemba Effect Through Phase Transitions

Holtzman¹,

Raz²

2022

Preprint

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“…In a more general context, the ME can be recast as "the initially further from equilibrium relaxes faster"with the separation from equilibrium being defined in a suitable way, see below. With such an interpretation, Mpemba-like effects have been investigated in a large variety of many-body systems: molecular gases [36,37], mixtures [38], granular gases [39][40][41][42][43][44], inertial suspensions [45,46], spin glasses [47], carbon nanotube resonators [48], clathrate hydrates [49], Markovian models [50][51][52][53][54], active systems [55], Ising models [56,57], non-Markovian mean-field systems [58,59], or quantum systems [60]. Also, it has been experimentally observed in colloids [61,62].…”

Section: Introductionmentioning

confidence: 99%

“…There have been two main approaches to the ME: the kinetic-theory or "thermal" approach [36][37][38][39][40][41][42][43][44][45][46] and the stochastic-process (or thermodynamics) or "entropic" approach [50][51][52][53][54][55][60][61][62]. In the thermal approach, kinetic theory makes it possible to define in a natural way an out-of-equilibrium time-dependent temperature T (t) (basically, the average kinetic energy).…”

Section: Introductionmentioning

confidence: 99%

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag

Megías,

Santos,

Prados

2022

Preprint

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Loosely speaking, the Mpemba effect appears when the hotter cools sooner or, in a more abstract way, when the further from equilibrium relaxes 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 Mpemba effect is analyzed via two alternative routes, recently considered in the literature. First, the kinetic or thermal route, in which the emergence of the Mpemba effect is marked by the crossing of the evolution curves of the kinetic temperature (average kinetic energy). Second, the stochastic thermodynamics or entropic route, in which the emergence of the Mpemba effect is marked by the crossing of the distance to equilibrium in probability space. A nonmutual correspondence between the thermal and entropic Mpemba effects is found in a certain region of parameters. Our theoretical description, 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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“…In fact, the statistical physics community is currently paying attention to Mpemba-like effects that have been described in a huge variety of complex systems in the last decades, such as ideal gases [41], molecular gases [42][43][44], mixtures [45], granular gases [46][47][48][49][50][51][52], inertial suspensions [53,54], spin glasses [55], Ising models [56][57][58], non-Markovian mean-field systems [59,60], carbon nanotube resonators [61], clathrate hydrates [62] , active systems [63], or quantum systems [64]. The theoretical approach to the fundamentals of the problem has been done via different routes like Markovian statistics [65][66][67][68][69] or Landau's theory of phase transitions [70]. Recently, in the context of a molecular gas under a nonlinear drag force, new interpretations and definitions of ME from thermal and entropic point of views, as well as a classification of the whole possible phenomenology, have been recently carried out [44].…”

Section: Introductionmentioning

confidence: 99%

Mpemba-like effect protocol for granular gases of inelastic and rough hard disks

Megías,

Santos

2022

Preprint

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We study the conditions under which a Mpemba-like effect emerges in granular gases of inelastic and rough hard disks driven by a class of thermostats characterized by the splitting of the noise intensity into translational and rotational counterparts. Thus, granular particles are affected by a stochastic force and a stochastic torque, which inject translational and rotational energy, respectively. We realize that a certain choice of a thermostat of this class can be characterized just by the total intensity and the fraction of noise transferred to the rotational degree of freedom with respect to the translational ones. Firstly, Mpemba effect is characterized by the appearance of a crossing between the temperature curves of the considered samples. Later, an overshoot of the temperature evolution with respect to the steadystate value is observed and the mechanism of Mpemba effect generation is changed. The election of parameters allows to design plausible protocols based on these thermostats for generating the initial states to observe the Mpemba-like effect in experiments. In order to obtain explicit results, we use a well-founded Maxwellian approximation for the evolution dynamics and the steady-state quantities. Finally, theoretical results are compared with direct simulation Monte Carlo and molecular dynamics results, and a very good agreement is found.

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Inducing and optimizing Markovian Mpemba effect with stochastic reset

Cited by 32 publications

References 56 publications

Landau Theory for the Mpemba Effect Through Phase Transitions

Landau Theory for the Mpemba Effect Through Phase Transitions

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag

Mpemba-like effect protocol for granular gases of inelastic and rough hard disks

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