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Christian Maes

Publications and source records attributed to Christian Maes.

At least 73 records · Page 4Linked to original sources
arXiv2019

Producing suprathermal tails in the stationary velocity distribution

We revisit effective scenarios for the origin of heavy tails in stationary velocity distributions. A first analysis combines localization with diffusive acceleration. That gets realized in space plasmas to find the so-called kappa-distributions having power-law decay at high speeds. There, localization at high energy already takes place for the reversible dynamics but becomes effective by an active diffusion in velocity space. A model for vibrating granular gases and giving rise to stretched exponential tails is also briefly discussed, where negative friction is the energizer. In all cases, the resulting nonMaxwellian velocity distributions are frenetically caused by the dependence on the speed of kinetic parameters.

cond-mat.stat-mech↗
arXiv2018

The asymptotic speed of reaction fronts in active reaction-diffusion systems

We study various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active Brownian processes in general spatial dimensions. Comparing 1D active branching processes with a passive counterpart (which has the same effective diffusion constant and reproduction rate), we find that the active process has a smaller propagation speed. In higher dimensions, a similar comparison yields the opposite conclusion.

cond-mat.stat-mech↗
arXiv2018

Death and resurrection of a current by disorder, interaction or activity

Because of disorder the current-field characteristic may show a first order phase transition as function of the field, at which the current jumps to zero when the driving exceeds a threshold. The discontinuity is caused by adding a finite correlation length in the disorder. At the same time the current may resurrect when the field is modulated in time, also discontinuously: a little shaking enables the current to jump up. Finally, in trapping models exclusion between particles postpones or even avoids the current from dying, while attraction may enhance it. We present simple models that illustrate those dynamical phase transitions in detail, and that allow full mathematical control.

cond-mat.stat-mech↗
arXiv2018

Active processes in one dimension

We consider the thermal and athermal overdamped motion of particles in 1D geometries where discrete internal degrees of freedom (spin) are coupled with the translational motion. Adding a driving velocity that depends on the time-dependent spin constitutes the simplest model of active particles (run-and-tumble processes) where the violation of the equipartition principle and of the Sutherland-Einstein relation can be studied in detail even when there is generalized reversibility. We give an example (with four spin values) where the irreversibility of the translational motion manifests itself only in higher-order (than two) time correlations. We derive a generalized telegraph equation as the Smoluchowski equation for the spatial density for an arbitrary number of spin values. We also investigate the Arrhenius exponential law for run-and-tumble particles, due to their activity the slope of the potential becomes important in contrast to the passive diffusion case and activity enhances the escape from a potential well (if that slope is high enough). Finally, in the absence of a driving velocity, the presence of internal currents such as in the chemistry of molecular motors may be transmitted to the translational motion and the internal activity is crucial for the direction of the emerging spatial current.

cond-mat.stat-mech↗
arXiv2017

Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation

We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a certain symmetry in the Hamiltonian, which extends earlier work that has connected the large-deviation behaviour of reversible stochastic processes to the gradient-flow structure of their deterministic limit. Natural examples of application include particle systems with inertia.

math.AP↗
arXiv2017

Non-reactive forces and pattern formation induced by a nonequilibrium medium

We study the induced interaction between multiple probes locally interacting with driven colloids and trapped in a toroidal geometry. The effective binary forces between the probes break the action-reaction principle and their range decreases with the driving. We demonstrate how in the stationary nonlinear nonequilibrium regime these interactions induce stability of a crystal-like pattern, where the probes are equidistant, when the probe-colloid interaction is either completely attractive or completely repulsive.

cond-mat.stat-mech↗
arXiv2017

Stabilization in the eye of a cyclone

We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around that center, where the induced force vanishes. We prove that the introduction of the rotational force in general enhances the stability of that point (and may turn it from unstable to stable!), starting at second-order in the nonequilibrium amplitude. When the driving is further enhanced the stabilization occurs for a wide range of rotation profiles and the induced stiffness converges to a universal expression proportional to the average mechanical stiffness. The model thus provides a rigorous example of stabilization of a fixed point due to contact with a nonequilibrium medium and beyond linear order around equilibrium.

cond-mat.stat-mech↗
arXiv2017

Midpoint distribution of directed polymers in the stationary regime: exact result through linear response

We obtain an exact result for the midpoint probability distribution function (pdf) of the stationary continuum directed polymer, when averaged over the disorder. It is obtained by relating that pdf to the linear response of the stochastic Burgers field to some perturbation. From the symmetries of the stochastic Burgers equation we derive a fluctuation-dissipation relation so that the pdf gets given by the stationary two space-time points correlation function of the Burgers field. An analytical expression for the latter was obtained by Imamura and Sasamoto [2013], thereby rendering our result explicit. In the large length limit that implies that the pdf is nothing but the scaling function $f_{\rm KPZ}(y)$ introduced by Prähofer and Spohn [2004]. Using the KPZ-universality paradigm, we find that this function can therefore also be interpreted as the pdf of the position y of the maximum of the Airy process minus a parabola and a two-sided Brownian motion. We provide a direct numerical test of the result through simulations of the Log-Gamma polymer.

cond-mat.dis-nn↗
arXiv2017

The induced motion of a probe coupled to a bath with random resettings

We consider a probe linearly coupled to the center of mass of a nonequilibrium bath. We study the induced motion on the probe for a model where a resetting mechanism is added to an overdamped bath dynamics with quadratic potentials. The fact that each bath-particle is at random times being reset to a fixed position is known for optimizing diffusive search strategies, but here stands for the nonequilibrium aspect of the bath. In the large bath scaling limit the probe is governed by an effective Langevin equation. Depending on the value of the parameters, there appear three regimes: (i) an equilibrium-like regime but with a reduced friction and an increased effective temperature; (ii) a regime where the noise felt by the probe is continuous but nonGaussian and exhibits fat-tails; (iii) a regime with a nonGaussian noise exhibiting power-law distributed jumps. The model thus represents an exactly solvable case for the origin of nonequilibrium probe dynamics.

cond-mat.stat-mech↗
arXiv2017

Life efficiency does not always increase with the dissipation rate

There does not exist a general positive correlation between important life-supporting properties and the entropy production rate. The simple reason is that nondissipative and time-symmetric kinetic aspects are also relevant for establishing optimal functioning. In fact those aspects are even crucial in the nonlinear regimes around equilibrium where we find biological processing on mesoscopic scales. We make these claims specific via examples of molecular motors, of circadian cycles and of sensory adaptation, whose performance in some regimes is indeed spoiled by increasing the dissipated power. We use the relation between dissipation and the amount of time-reversal breaking to keep the discussion quantitative also in effective models where the physical entropy production is not clearly identifiable.

cond-mat.stat-mech↗
arXiv2017

Tension and chemical efficiency of Myosin-II motors

Recent experiments demonstrate that molecular motors from the Myosin II family serve as cross-links inducing active tension in the cytoskeletal network. Here we revise the Brownian ratchet model, previously studied in the context of active transport along polymer tracks, in setups resembling a motor in a polymer network, also taking into account the effect of electrostatic changes in the motor heads. We explore important mechanical quantities and show that such a model is also capable of mechanosensing. Finally, we introduce a novel efficiency based on excess heat production by the chemical cycle which is directly related to the active tension the motor exerts. The chemical efficiencies differ considerably for motors with a different number of heads, while their mechanical properties remain qualitatively similar. For motors with a small number of heads, the chemical efficiency is maximal when they are frustrated, a trait that is not found in larger motors.

physics.bio-ph↗
arXiv2017

Non-dissipative effects in nonequilibrium systems

Studying the role of activity parameters and the nature of time-symmetric path-variables constitutes an important part of nonequilibrium physics, so we argue. The relevant variables are residence times and the undirected traffic between different states. Parameters are the reactivities, escape rates and accessibilities and how those possibly depend on the imposed driving. All those count in the frenetic contribution to statistical forces, response and fluctuations, operational even in the stationary distribution when far enough from equilibrium. As these time-symmetric aspects can vary independently from the entropy production we call the resulting effects non-dissipative, ranking among features of nonequilibrium that have traditionally not been much included in statistical mechanics until recently. Those effects can be linked to localization such as in negative differential conductivity, in jamming or glassy behavior or in the slowing down of thermalization. Activities may decide the direction of physical currents away from equilibrium, and the nature of the stationary distribution, including its population inversion, is not as in equilibrium decided by energy-entropy content. The ubiquity of non-dissipative effects and of that frenetic contribution in theoretical considerations invites a more operational understanding and statistical forces outside equilibrium appear to provide such a frenometry.

cond-mat.stat-mech↗
arXiv2017

Deriving GENERIC from a generalized fluctuation symmetry

Much of the structure of macroscopic evolution equations for relaxation to equilibrium can be derived from symmetries in the dynamical fluctuations around the most typical trajectory. For example, detailed balance as expressed in terms of the Lagrangian for the path-space action leads to gradient zero-cost flow. We find a new such fluctuation symmetry that implies GENERIC, an extension of gradient flow where a Hamiltonian part is added to the dissipative term in such a way as to retain the free energy as Lyapunov function.

cond-mat.stat-mech↗
arXiv2017

Frenetic bounds on the entropy production

We show that under local detailed balance the expected entropy production rate is always bounded in terms of the dynamical activity. The activity refers to the time-symmetric contribution in the action functional for path-space probabilities and relates to escape rates and unoriented traffic. Under global detailed balance we get a lower bound on the decrease of free energy which is known from gradient flow analysis. For stationary driven systems we recover some of the recently studied "uncertainty" relations for the entropy production, appearing in studies about the effectiveness of mesoscopic machines and that refine the positivity of the entropy production rate by providing lower bounds in terms of a positive and even function of the current(s). We extend these lower bounds for the entropy production rate to include underdamped diffusions.

cond-mat.stat-mech↗
arXiv2016

The modified Langevin description for probes in a nonlinear medium

When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is not longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.

cond-mat.soft↗
arXiv2016

Nonequilibrium physics aspects of probabilistic cellular automata

Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from time-symmetric PCA, satisfying detailed balance, and we give their Kubo formula for linear response. Close-to-detailed balance we investigate the form of the McLennan distribution and the minimum entropy production principle. More generally, when time-symmetry is broken in the stationary process, there is a fluctuation symmetry for a corresponding entropy flux. For linear response around nonequilibria we also give the appropriate formula which is now not only entropic in nature.

cond-mat.stat-mech↗
arXiv2016

What decides the direction of a current?

Nonequilibria show currents that are maintained as the result of a steady driving. We ask here what decides their direction. It is not only the second law, or the positivity of the entropy production that decides; also non-dissipative aspects often matter and sometimes completely decide.

cond-mat.stat-mech↗