Comment on "Entropy Production and Fluctuation Theorems for Active Matter"
This is a comment to a letter by D. Mandal, K. Klymko and M. R. DeWeese published as Phys. Rev. Lett. 119, 258001 (2017).
cond-mat.stat-mech↗
arXiv subjects
U. Marini Bettolo Marconi
Publications and source records attributed to U. Marini Bettolo Marconi.
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 re-orientation time and $ξ$ the width characterising the surface's smoothness ($ξ\to 0$ 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.
cond-mat.soft↗
Non-equilibrium 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.
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Models of granular ratchets
We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Boltzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement is observed.
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Noise Rectification and Fluctuations of an Asymmetric Inelastic Piston
We consider a massive inelastic piston, whose opposite faces have different coefficients of restitution, moving under the action of an infinitely dilute gas of hard disks maintained at a fixed temperature. The dynamics of the piston is Markovian and obeys a continuous Master Equation: however, the asymmetry of restitution coefficients induces a violation of detailed balance and a net drift of the piston, as in a Brownian ratchet. Numerical investigations of such non-equilibrium stationary state show that the velocity fluctuations of the piston are symmetric around the mean value only in the limit of large piston mass, while they are strongly asymmetric in the opposite limit. Only taking into account such an asymmetry, i.e. including a third parameter in addition to the mean and the variance of the velocity distribution, it is possible to obtain a satisfactory analytical prediction for the ratchet drift velocity.
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Lattice Boltzmann method for inhomogeneous fluids
We present a lattice-based numerical method to describe the non equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting from a microscopic description of the system. It involves a series of approximations which are similar to those employed in theories of inhomogeneous fluids, such as Density Functional theory. Among the merits of the present approach: the possibility to determine the equation of state of the model, the transport coefficients and to provide an efficient method of numerical solution under non-uniform conditions. The algorithm is tested in a particular non equilibrium situation, namely the steady flow of a hard-sphere fluid across a narrow slit. Pronounced non-hydrodynamic oscillations in the density and velocity profiles are found.
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Velocity fluctuations in a one dimensional Inelastic Maxwell model
We consider the velocity fluctuations of a system of particles described by the Inelastic Maxwell Model. The present work extends the methods, previously employed to obtain the one-particle velocity distribution function, to the study of the two particle correlations. Results regarding both the homogeneous cooling process and the steady state driven regime are presented. In particular we obtain the form of the pair correlation function in the scaling region of the homogeneous cooling process and show that some of its moments diverge. This fact has repercussions on the behavior of the energy fluctuations of the model.
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Generalized Casimir forces in non-equilibrium systems
In the present work we propose a method to determine fluctuation induced forces in non equilibrium systems. These forces are the analogue 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 non equilibrium systems exhibit long-range correlations and the associated structure factors diverge in the long wavelength limit. The introduction of external bodies into such systems in general modifies the spectrum of these fluctuations and leads to the appearance of a net force between these bodies. The mechanism is illustrated by means of a simple example: a reaction diffusion equation with random noises.
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Fluctuation-Induced Casimir Forces in Granular Fluids
We have numerically investigated the behavior of driven non-cohesive granular media and found 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.
cond-mat.stat-mech↗
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 the 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 clusterizes. Such a phenomenon is not instantaneous, but is characterized by a time scale, $τ$, 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.
cond-mat.stat-mech↗
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 which 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. Comparison with previous studies are presented.
cond-mat.stat-mech↗
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 which displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere 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 area/volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed.
cond-mat.stat-mech↗
Dynamical properties of vibrofluidized granular mixtures
Motivated by recent experiments we have carried out an Event Driven computer simulation of a diluted binary mixture of granular particles vertically vibrated in the presence of gravity. The simulations not only confirm that the kinetic energies of the two species are not equally distributed, as predicted by various theoretical models, but also seem to reproduce rather well the density and temperature profiles measured experimentally. Rotational degrees of freedom do not seem to play any important qualitative role. Instead, simulation shows the onset of a clustering instability along the horizontal direction. At the interior of the cluster we observe a secondary instability with respect to the perfect mixing situation, so that segregation of species is observed within the cluster.
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Driven low density granular mixtures
We study the steady state properties of a 2D granular mixture in the presence of energy driving by employing simple analytical estimates and Direct Simulation Monte Carlo. We adopt two different driving mechanisms: a) a homogeneous heat bath with friction and b) a vibrating boundary (thermal or harmonic) in the presence of gravity. The main findings are: the appearance of two different granular temperatures, one for each species; the existence of overpopulated tails in the velocity distribution functions and of non trivial spatial correlations indicating the spontaneous formation of cluster aggregates. In the case of a fluid subject to gravity and to a vibrating boundary, both densities and temperatures display non uniform profiles along the direction normal to the wall, in particular the temperature profiles are different for the two species while the temperature ratio is almost constant with the height. Finally, we obtained the velocity distributions at different heights and verified the non gaussianity of the resulting distributions.
cond-mat.stat-mech↗
Influence of correlations on the velocity statistics of scalar granular gases
The free evolution of inelastic particles in one dimension is studied by means of Molecular Dynamics (MD), of an inelastic pseudo-Maxwell model and of a lattice model, with emphasis on the role of spatial correlations. We present an exact solution of the 1d granular pseudo-Maxwell model for the scaling distribution of velocities and discuss how this model fails to describe correctly the homogeneous cooling stage of the 1d granular gas. Embedding the pseudo-Maxwell gas on a lattice (hence allowing for the onset of spatial correlations), we find a much better agreement with the MD simulations even in the inhomogeneous regime. This is seen by comparing the velocity distributions, the velocity profiles and the structure factors of the velocity field.
cond-mat.stat-mech↗
Cooling of a lattice granular fluid as an ordering process
We present a new 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. In spite of its simplicity, it features several different 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, persistence, 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.
cond-mat.stat-mech↗
Driven granular gases with gravity
We study fluidized granular gases in a stationary state determined by the balance between an external driving and the bulk dissipation. The two considered situations are inspired by recent experiments, where the 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 which are in good agreement with the experiments. Moreover we measure the velocity distributions which 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.
cond-mat.stat-mech↗
A microscopic model for solidification
We present a novel picture of a non isothermal solidification process starting from a molecular level, where the microscopic origin of the basic mechanisms and of the instabilities characterizing the approach to equilibrium is rendered more apparent than in existing approaches based on coarse grained free energy functionals à la Landau. The system is composed by a lattice of Potts spins, which change their state according to the stochastic dynamics proposed some time ago by Creutz. Such a method is extended to include the presence of latent heat and thermal conduction. Not only the model agrees with previous continuum treatments, but it allows to introduce in a consistent fashion the microscopic stochastic fluctuations. These play an important role in nucleating the growing solid phase in the melt. The approach is also very satisfactory from the quantitative point of view since the relevant growth regimes are fully characterized in terms of scaling exponents.
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