Memory effect in uniformly heated granular gases

Enhancing Otto refrigerator performance with a precooling strategy

The precooling strategy, which leads to exponentially faster heating, is a counterintuitive relaxation phenomenon wherein cooling the system before heating it dramatically shortens the relaxation time. We investigate the performance of a Markovian system functioning as an Otto refrigerator for a finite time, incorporating a precooling stage before the cyclic heating process. Our results demonstrate that precooling prior to the heating process in the Otto cycle optimizes the machine's performance by significantly enhancing the machine performance and the stability of the refrigerator.

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.

Kinetic glass transition in granular gases and nonlinear molecular fluids

In this paper, we investigate, both analytically and numerically, the emergence of a kinetic glass transition in two different model systems: a uniformly heated granular gas and a molecular fluid with nonlinear drag. Despite the profound differences between these two physical systems, their behavior in thermal cycles share strong similarities, which stem from the relaxation time diverging algebraically at low temperatures for both systems. When the driving intensity--for the granular gas-or the bath temperature-for the molecular fluid-is decreased to sufficiently low values, the kinetic temperature of both systems becomes "frozen" at a value that depends on the cooling rate through a power law with the same exponent. Interestingly, this frozen glassy state is universal in the following sense: for a suitable rescaling of the relevant variables, its velocity distribution function becomes independent of the cooling rate. Upon reheating, i.e., when either the driving intensity or the bath temperature is increased from this frozen state, hysteresis cycles arise and the apparent heat capacity displays a maximum. The numerical results obtained from the simulations are well described by a perturbative approach.

Strain-driven Kovacs-like memory effect in glasses

Studying complex relaxation behaviors is of critical importance for understanding the nature of glasses. Here we report a Kovacs-like memory effect in glasses, manifested by non-monotonic stress relaxation during two-step high-to-low strains stimulations. During the stress relaxation process, if the strain jumps from a higher state to a lower state, the stress does not continue to decrease, but increases first and then decreases. The memory effect becomes stronger when the atomic motions become highly collective with a large activation energy, e.g. the strain in the first stage is larger, the temperature is higher, and the stimulation is longer. The physical origin of the stress memory effect is studied based on the relaxation kinetics and the in-situ synchrotron X-ray experiments. The stress memory effect is probably a universal phenomenon in different types of glasses.

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.

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously-from a mathematical point of view-prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.

Linear response in the uniformly heated granular gas

We analyze the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the nonequilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the "direct" relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearize the evolution equations around the steady state, but we also derive generalized out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behavior of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of an anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behavior. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found.

Memory effects in glasses: Insights into the thermodynamics of out-of-equilibrium systems revealed by a simple model of the Kovacs effect

Glasses are interesting materials because they allow us to explore the puzzling properties of out-of-equilibrium systems. One of them is the Kovacs effect in which a glass, brought to an out-of-equilibrium state in which all its thermodynamic variables are identical to those of an equilibrium state, nevertheless evolves, showing a hump in some global variable before the thermodynamic variables come back to their starting point. We show that a simple three-state system is sufficient to study this phenomenon using numerical integrations and exact analytical calculations. It also brings some light on the concept of fictive temperature, often used to extend standard thermodynamics to the out-of-equilibrium properties of glasses. We confirm that the concept of a unique fictive temperature is not valid, an show it can be extended to make a connection with the various relaxation processes in the system. The model also brings further insights on the thermodynamics of out-of-equilibrium systems. Moreover, we show that the three-state model is able to describe various effects observed in glasses such as the asymmetric relaxation to equilibrium discussed by Kovacs, or the reverse crossover measured on B_{2}O_{3}.

Ballistic propagation of density correlations and excess wall forces in quenched granular media

We investigate a granular gas in a shaken quasi-two-dimensional box in molecular dynamics computer simulations. After a sudden change (quench) of the shaking amplitude, transient density correlations are observed orders of magnitude beyond the steady-state correlation length scale. Propagation of the correlations is ballistic, in contrast to recently investigated quenches of Brownian particles that show diffusive propagation [Rohwer et al., Phys. Rev. Lett. 118, 015702 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.015702, Rohwer et al., Phys. Rev. E 97, 032125 (2018)2470-004510.1103/PhysRevE.97.032125]. At sufficiently strong cooling of the fluid the effect is overlaid by clustering instability of the homogeneous cooling state with different scaling behavior. We are able to identify different quench regimes. In each regime correlations exhibit remarkably universal position dependence. In simulations performed with side walls we find confinement effects for temperature and pressure in steady-state simulations and an additional transient wall pressure contribution when changing the shaking amplitude. The transient contribution is ascribed to enhanced relaxation of the fluid in the presence of walls. From incompatible scaling behavior we conclude that the observed effects with and without side walls constitute distinct phenomena.

Induced correlations and rupture of molecular chaos by anisotropic dissipative Janus hard disks

A system of smooth "frozen" Janus-type disks is studied. Such disks cannot rotate and are divided by their diameter into two sides of different inelasticities. Taking as a reference a system of colored elastic disks, we find differences in the behavior of the collisions once the anisotropy is included. A homogeneous state, akin to the homogeneous cooling state of granular gases, is seen to arise and the singular behavior of both the collisions and the precollisional correlations are highlighted.

Large Mpemba-like effect in a gas of inelastic rough hard spheres

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.

Nonequilibrium steady states, coexistence, and criticality in driven quasi-two-dimensional granular matter

Nonequilibrium steady states of vibrated inelastic frictionless spheres are investigated in quasi-two-dimensional confinement via molecular dynamics simulations. The phase diagram in the density-amplitude plane exhibits a fluidlike disordered and an ordered phase with threefold symmetry, as well as phase coexistence between the two. A dynamical mechanism exists that brings about metastable traveling clusters and at the same time stable clusters with anisotropic shapes at low vibration amplitude. Moreover, there is a square bilayer state which is connected to the fluid by BKTHNY-type two-step melting with an intermediate tetratic phase. The critical behavior of the two continuous transitions is studied in detail. For the fluid-tetratic transition, critical exponents of γ[over ̃]=1.73, η_{4}≈1/4, and z=2.05 are obtained.

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component i to be approximately proportional to 2σ_{i}+〈σ〉, where σ_{i} is the diameter of the disk and 〈σ〉 is the mean diameter.

Giant Kovacs-Like Memory Effect for Active Particles

Dynamical properties of self-propelled particles obeying a bounded confidence rule are investigated by means of kinetic theory and agent-based simulations. While memory effects are observed in disordered systems, we show that they also occur in active matter systems. In particular, we find that the system exhibits a giant Kovacs-like memory effect that is much larger than predicted by a generic linear theory. Based on a separation of time scales we develop a nonlinear theory to explain this effect. We apply this theory to driven granular gases and propose further applications to spin glasses.

When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids

Under certain conditions, two samples of fluid at different initial temperatures present a counterintuitive behavior known as the Mpemba effect: it is the hotter system that cools sooner. Here, we show that the Mpemba effect is present in granular fluids, both in uniformly heated and in freely cooling systems. In both cases, the system remains homogeneous, and no phase transition is present. Analytical quantitative predictions are given for how differently the system must be initially prepared to observe the Mpemba effect, the theoretical predictions being confirmed by both molecular dynamics and Monte Carlo simulations. Possible implications of our analysis for other systems are also discussed.

Global stability and H theorem in lattice models with nonconservative interactions

In kinetic theory, a system is usually described by its one-particle distribution function f(r,v,t), such that f(r,v,t)drdv is the fraction of particles with positions and velocities in the intervals (r,r+dr) and (v,v+dv), respectively. Therein, global stability and the possible existence of an associated Lyapunov function or H theorem are open problems when nonconservative interactions are present, as in granular fluids. Here, we address this issue in the framework of a lattice model for granularlike velocity fields. For a quite general driving mechanism, including both boundary and bulk driving, we show that the steady state reached by the system in the long-time limit is globally stable. This is done by proving analytically that a certain H functional is nonincreasing in the long-time limit. Moreover, for a quite general energy injection mechanism, we are able to demonstrate that the proposed H functional is nonincreasing for all times. Also, we put forward a proof that clearly illustrates why the "classical" Boltzmann functional H_{B}[f]=∫drdvf(r,v,t)lnf(r,v,t) is inadequate for systems with nonconservative interactions. This is done not only for the simplified kinetic description that holds in the lattice models analyzed here but also for a general kinetic equation, like Boltzmann's or Enskog's.

Memory effects in the relaxation of a confined granular gas

The accuracy of a model to describe the horizontal dynamics of a confined quasi-two-dimensional system of inelastic hard spheres is discussed by comparing its predictions for the relaxation of the temperature in a homogenous system with molecular dynamics simulation results for the original system. A reasonably good agreement is found. Next the model is used to investigate the peculiarities of the nonlinear evolution of the temperature when the parameter controlling the energy injection is instantaneously changed while the system was relaxing. This can be considered as a nonequilibrium generalization of the Kovacs effect. It is shown that, in the low-density limit, the effect can be accurately described by using a simple kinetic theory based on the first Sonine approximation for the one-particle distribution function. Some possible experimental implications are indicated.