Entropy production and collective excitations of crystals out of equilibrium: The concept of entropons.

We study the collective vibrational excitations of crystals under out-of-equilibrium steady conditions that give rise to entropy production. Their excitation spectrum comprises equilibriumlike phonons of thermal origin and additional collective excitations called entropons because each of them represents a mode of spectral entropy production. Entropons coexist with phonons and dominate them when the system is far from equilibrium while they are negligible in near-equilibrium regimes. The concept of entropons has been recently introduced and verified in a special case of crystals formed by self-propelled particles. Here we show that entropons exist in a broader class of active crystals that are intrinsically out of equilibrium and characterized by the lack of detailed balance. After a general derivation, several explicit examples are discussed, including crystals consisting of particles with alignment interactions and frictional contact forces.

Spontaneous Velocity Alignment in Motility-Induced Phase Separation.

We study a system of purely repulsive spherical self-propelled particles in the minimal setup inducing motility-induced phase separation (MIPS). We show that, even if explicit alignment interactions are absent, a growing order in the velocities of the clustered particles accompanies MIPS. Particles arrange into aligned or vortexlike domains whose size increases as the persistence of the self-propulsion grows, an effect that is quantified studying the spatial correlation function of the velocities. We explain the velocity alignment by unveiling a hidden alignment interaction of the Vicsek-like form, induced by the interplay between steric interactions and self-propulsion.

Effective equilibrium states in mixtures of active particles driven by colored noise.

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

Self-propulsion against a moving membrane: Enhanced accumulation and drag force.

Self-propulsion (SP) is a main feature of active particles (AP), such as bacteria or biological micromotors, distinguishing them from passive colloids. A renowned consequence of SP is accumulation at static interfaces, even in the absence of hydrodynamic interactions. Here we address the role of SP in the interaction between AP and a moving semipermeable membrane. In particular, we implement a model of noninteracting AP in a channel crossed by a partially penetrable wall, moving at a constant velocity c. With respect to both the cases of passive colloids with c>0 and AP with c=0, the AP with finite c show enhancement of accumulation in front of the obstacle and experience a largely increased drag force. This effect is understood in terms of an effective potential localised at the interface between particles and membrane, of height proportional to cτ/ξ, where τ is the AP's reorientation time and ξ the width characterizing the surface's smoothness (ξ→0 for hard core obstacles). An approximate analytical scheme is able to reproduce the observed density profiles and the measured drag force, in very good agreement with numerical simulations. The effects discussed here can be exploited for automatic selection and filtering of AP with desired parameters.

Critical phenomena in active matter.

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a φ^{4} scalar field theory subject to an exponentially correlated noise, we exploit the unified colored-noise approximation to map the nonequilibrium active dynamics onto an effective equilibrium one. This allows us to follow the evolution of the second-order critical point as a function of the noise parameters: the correlation time τ and the noise strength D. Our results suggest that the universality class of the model remains unchanged. We also estimate the effect of Gaussian fluctuations on the mean-field approximation finding an Ornstein-Zernike-like expression for the static structure factor at long wavelengths. Finally, to assess the validity of our predictions, we compare the mean-field theoretical results with numerical simulations of active Lennard-Jones particles in two and three dimensions, finding good qualitative agreement at small τ values.

Nonequilibrium fluctuations in a driven stochastic Lorentz gas.

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production Δs(tot). One is the entropy production of the medium Δs(m), which is equal to the energy exchanged with the scatterers, divided by a parameter θ, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by θ. At small E, a good collapse of the two distributions is found: in this case, the two quantities also verify the fluctuation relation (FR), indicating that both are good approximations of Δs(tot). Differently, for large values of E, the fluctuations of W violate the FR, while Δs(m) still verifies it.

Generalized Casimir forces in nonequilibrium systems.

In the present work, we propose a method to determine fluctuation-induced forces in nonequilibrium systems. These forces are the analog of the well-known Casimir forces, which were originally introduced in quantum field theory and later extended to the area of critical phenomena. The procedure starts from the observation that many nonequilibrium systems exhibit fluctuations with macroscopic correlation lengths, and the associated structure factors strongly depend on the wave vectors for long wavelengths; in some cases the correlations become long range, and the structure factors show algebraic divergences in the long-wavelength limit. The introduction of external bodies into such systems in general modifies the spectrum of these fluctuations, changing the value of the renormalized pressure, which becomes inhomogeneous. This inhomogeneous pressure leads to the appearance of a net force between the external bodies. It is shown that the force can be obtained from the knowledge of the structure factor of the homogeneous system. The mechanism is illustrated by means of a simple example: a reaction-diffusion equation, where the correlation function has a characteristic length. The role of this length in the Casimir force is elucidated.

Fluctuation-induced casimir forces in granular fluids.

We numerically investigate the behavior of driven noncohesive granular media and find that two fixed large intruder particles, immersed in a sea of small particles, experience, in addition to a short-range depletion force, a long-range repulsive force. The observed long-range interaction is fluctuation-induced and we propose a mechanism similar to the Casimir effect that generates it: The hydrodynamic fluctuations are geometrically confined between the intruders, producing an unbalanced renormalized pressure. An estimation based on computing the possible Fourier modes explains the repulsive force and is in qualitative agreement with the simulations.

Dynamics of vibrofluidized granular gases in periodic structures.

The behavior of a driven granular gas in a container consisting of M connected compartments is studied employing a microscopic kinetic model. After obtaining the governing equations for the occupation numbers and the granular temperatures of each compartment we consider the various dynamical regimes. The system displays interesting analogies with the ordering processes of phase separating mixtures quenched below their critical point. In particular, we show that below a certain value of the driving intensity the populations of the various compartments become unequal and the system forms clusters. Such a phenomenon is not instantaneous, but is characterized by a time scale tau which follows a Vogel-Vulcher exponential behavior. On the other hand, the reverse phenomenon which involves the "evaporation" of a cluster due to the driving force is also characterized by a second time scale which diverges at the limit of stability of the cluster.

Statistical mechanics of granular gases in compartmentalized systems.

We study the behavior of an assembly of N granular particles contained in two compartments within a simple kinetic approach. The particles belonging to each compartment collide inelastically with each other and are driven by a stochastic heat bath. In addition, the fastest particles can change compartment at a rate that depends on their kinetic energy. Via a Boltzmann velocity distribution approach, we first study the dynamics of the model in terms of a coupled set of equations for the populations in the containers and their granular temperatures and find a crossover from a symmetric high-temperature phase to an asymmetric low-temperature phase. Finally, in order to include statistical fluctuations, we solve the model within the direct simulation Monte Carlo approach. Comparisons with previous studies are presented.

Surface and capillary transitions in an associating binary mixture model.

We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram that displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere with the physical mechanism involved in the appearance of these phase diagrams, leading to an enhanced tendency to phase separate below the lower critical solution point. Three different cases are considered: a planar solid surface in contact with a bulk fluid, while the other two represent two models of porous systems, namely, a slit and an array on infinitely long parallel cylinders. We confirm that surface transitions, as well as capillary transitions for a large surface area to volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed.

Barkas effect for antiproton stopping in H2.

We report the stopping power of molecular hydrogen for antiprotons of kinetic energy above the maximum (approximately 100 keV) with the purpose of comparing with the proton one. Our result is consistent with a positive difference in antiproton-proton stopping powers above approximately 250 keV and with a maximum difference between the stopping powers of 21%+/-3% at around 600 keV.

Cooling of a lattice granular fluid as an ordering process.

We present a microscopic model of granular medium to study the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions on the velocity field. In spite of its simplicity and intrinsic limitations, it features several aspects of the rich phenomenology observed in granular materials and allows to make contact with other topics of statistical mechanics such as diffusion processes, domain growth, aging phenomena. Interestingly, while local observables, being controlled by the largest wavelength fluctuations, seem to suggest a purely diffusive behavior, the formation of spatially extended structures and topological defects, such as vortices and shocks, reveals a more complex scenario. Finally, only for quasielastic systems, we observe a neat scale separation, which represents a fundamental hypothesis to develop a granular hydrodynamics.

Driven granular gases with gravity.

We study fluidized granular gases in a stationary state determined by the balance between external driving and bulk dissipation. The two considered situations are inspired by recent experiments, where gravity plays a major role as a driving mechanism: in the first case, gravity acts only in one direction and the bottom wall is vibrated; in the second case, gravity acts in both directions and no vibrating walls are present. Simulations performed under the molecular chaos assumption show averaged profiles of density, velocity, and granular temperature that are in good agreement with the experiments. Moreover, we measure velocity distributions that show strong non-Gaussian behavior, as experiments pointed out, but also density correlations accounting for clustering, at odds with the experimental results. The hydrodynamics of the first model is discussed and an exact solution is found for the density and granular temperature as functions of the distance from the vibrating wall. The limitations of such a solution, in particular in a broad layer near the wall injecting energy, are discussed.

Kinetic approach to granular gases.

We address the problem of the so-called "granular gases," i.e., gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which inject energies. These models exhibit a genuine thermodynamic limit, i.e., at fixed density the mean values of kinetic energy and dissipated energy per particle are independent of the number N of particles, for large values of N. One has two regimes: when the typical relaxation time tau of the driving Brownian process is small compared with the mean collision time tau(c) the spatial density is nearly homogeneous and the velocity probability distribution is Gaussian. In the opposite limit tau>>tau(c) one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the Gaussian one. Simulations performed in one and two dimensions under the Stosszahlansatz Boltzmann approximation confirm the scenario. Furthermore, we analyze the instabilities bringing to the spatial and the velocity clusterization. Firstly, in the framework of a mean-field model, we explain how the existence of the inelasticity can lead to a spatial clusterization; on the other hand, we discuss, in the framework of a Langevin dynamics treating the collisions in a mean-field way, how a non-Gaussian distribution of velocity can arise. The comparison between the numerical and the analytical results exhibits an excellent agreement.