arXiv subjects

Christian Maes

Publications and source records attributed to Christian Maes.

At least 91 records · Page 5Linked to original sources

arXiv2016

Driving-induced stability with long-range effects

We give a sufficient condition under which an applied rotation on medium particles stabilizes a slow probe in the rotation center. The symmetric part of the stiffness matrix thus gets a positive Lamb shift with respect to equilibrium. For illustration we take diffusive medium particles with a self-potential in the shape of a Mexican hat, high around the origin. There is a short-range attraction between the medium particles and the heavier probe, all immersed in an equilibrium thermal bath. For no or small rotation force on the medium particles, the origin is an unstable fixed point for the probe and the precise shape of the self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold, while the medium particles are still repelled from the origin, the probe stabilizes there and more details of the medium-density at large distance start to matter. The effect is robust around the quasi-static limit with rotation threshold only weakly depending on the temperature but the stabilization gets stronger at lower temperatures.

cond-mat.stat-mech↗

arXiv2015

Statistical forces from close--to--equilibrium media

We discuss the physical meaning and significance of statistical forces on quasi-static probes in first order around detailed balance for driven media. Exploiting the quasi-static energetics and the structure of (McLennan) steady nonequilibrium ensembles, we find that the statistical force obtains a nonequilibrium correction deriving from the excess work of driving forces on the medium in its relaxation after probe displacement. This reformulates, within a more general context, the recent result by N. Nakagawa (Phys. Rev. E 90, 022108 (2014)) on thermodynamic aspects of weakly nonequilibrium adiabatic pumping. It also proposes a possible operational tool for accessing some excess quantities in steady state thermodynamics. Furthermore, we show that the point attractors of a (macroscopic) probe coupled to a weakly driven medium realize the predictions of the minimum entropy production principle. Finally, we suggest a method to measure the relative dynamical activity through different transition channels, via the measurement of the statistical force induced by a suitable driving.

cond-mat.stat-mech↗

arXiv2015

Nonequilibrium Response and Frenesy

We present examples of how time-symmetric kinetic factors contribute to the response either in nonlinear order around equilibrium or in linear order around nonequilibrium. The phenomenology we associate to that so called frenetic contribution are negative differential conductivity, changes in the Einstein relation between friction and noise, and population inversion.

cond-mat.stat-mech↗

arXiv2015

No information or horizon paradoxes for Th. Smiths

'Th'e 'S'tatistical 'm'echanician 'i'n 'th'e 's'treet (our Th. Smiths) must be surprised upon hearing popular versions of some of today's most discussed paradoxes in astronomy and cosmology. In fact, rather standard reminders of the meaning of thermal probabilities in statistical mechanics appear to answer the horizon problem (one of the major motivations for inflation theory) and the information paradox (related to black hole physics), at least as they are usually presented. Still the paradoxes point to interesting gaps in our statistical understanding of (quantum) gravitational effects.

physics.pop-ph↗

arXiv2015

How statistical forces depend on thermodynamics and kinetics of driven media

We study the statistical force of a nonequilibrium environment on a quasi-static probe. In the linear regime the isothermal work on the probe equals the excess work for the medium to relax to its new steady condition with displaced probe. Also the relative importance of reaction paths can be measured via statistical forces, and from second order onwards the force on the probe reveals information about nonequilibrium changes in the reactivity of the medium. We also show that statistical forces for nonequilibrium media are generally nonadditive, in contrast with the equilibrium situation. Both the presence of non-thermodynamic corrections to the forces and their nonadditivity put serious constraints on any formulation of nonequilibrium steady state thermodynamics.

cond-mat.stat-mech↗

arXiv2015

Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics

Glansdorff and Prigogine (1970) proposed a decomposition of the entropy production rate, which today is mostly known for Markov processes as the Hatano-Sasa approach. Their context was irreversible thermodynamics which, while ignoring fluctuations, still allows a somewhat broader treatment than the one based on the Master or Fokker-Planck equation. Glansdorff and Prigogine were the first to introduce a notion of excess entropy production rate $δ^2$EP and they suggested as sufficient stability criterion for a nonequilibrium macroscopic condition that $δ^2$EP be positive. We find for nonlinear diffusions that their excess entropy production rate is itself the time-derivative of a local free energy which is the close-to-equilibrium functional governing macroscopic fluctuations. The positivity of the excess $δ^2$EP, for which we state a simple sufficient condition, is therefore equivalent with the monotonicity in time of that functional in the relaxation to steady nonequilibrium. There also appears a relation with recent extensions of the Clausius heat theorem close-to-equilibrium. The positivity of $δ^2$EP immediately implies a Clausius (in)equality for the excess heat. A final and related question concerns the operational meaning of fluctuation functionals, nonequilibrium free energies, and how they make their entrée in irreversible thermodynamics.

cond-mat.stat-mech↗

arXiv2015

Frenetic aspects of second order response

Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called frenetic contribution in second order around equilibrium is illustrated in different physical examples, such as for non-thermodynamic aspects in the coupling between system and reservoir, for the dependence on disorder in dielectric response and for the nonlinear correction to the Sutherland--Einstein relation. More generally, the way in which a system's dynamical activity changes by the pertubation is visible (only) from nonlinear response.

cond-mat.stat-mech↗

arXiv2015

Locality and nonlocality of classical restrictions of quantum spin systems with applications to quantum large deviations and entanglement

We study the projection on classical spins starting from quantum equilibria. We show Gibbsianness or quasi-locality of the resulting classical spin system for a class of gapped quantum systems at low temperatures including quantum ground states. A consequence of Gibbsianness is the validity of a large deviation principle in the quantum system which is known and here recovered in regimes of high temperature or for thermal states in one dimension. On the other hand we give an example of a quantum ground state with strong nonlocality in the classical restriction, giving rise to what we call measurement induced entanglement, and still satisfying a large deviation principle.

math-ph↗

arXiv2014

On the kinetics that moves Myosin V

Molecular motor proteins such as Myosin V, Dynein or Kinesin are no ratchets, at least not with a flashing asymmetric potential; the crucial asymmetry is in the dynamical activity. We make that explicit in terms of a simple Markov model, emphasizing the kinetic (and non-thermodynamic) aspects of stochastic transport. The analysis shows the presence of a fluctuation symmetry in that part of the dynamical activity which is antisymmetric under reversal of trailing and leading head of the motor. The direction of the motor motion is determined by it.

cond-mat.stat-mech↗

arXiv2014

Friction and noise for a probe in a nonequilibrium fluid

We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation dissipation relation between friction and noise for probe motion in a nonequilibrium fluid

cond-mat.stat-mech↗

arXiv2014

Thermal response in driven diffusive systems

Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast relaxing mechanical, chemical or thermal equilibrium reservoirs. Modifying one of the temperatures creates both entropy fluxes and changes in dynamical activity. That is not unlike mechanical response of nonequilibrium systems but the extra difficulty for perturbation theory via path-integration is that for a Langevin dynamics temperature also affects the noise amplitude and not only the drift part. Using a discrete-time mesh adapted to the numerical integration one avoids that ultraviolet problem and we arrive at a fluctuation expression for its thermal susceptibility. The algorithm appears stable under taking even finer resolution.

cond-mat.stat-mech↗

arXiv2014

Mobility transition in a dynamic environment

Depending on how the dynamical activity of a particle in a random environment is influenced by an external field $E$, its differential mobility at intermediate $E$ can turn negative. We discuss the case where for slowly changing random environment the driven particle shows negative differential mobility while that mobility turns positive for faster environment changes. We illustrate this transition using a 2D-lattice Lorentz model where a particle moves in a background of simple exclusion walkers. The effective escape rate of the particle (or minus its collision frequency) which is essential for its mobility-behavior depends both on $E$ and on the kinetic rate $γ$ of the exclusion walkers. Large $γ$, i.e., fast obstacle motion, amounts to merely rescaling the particle's free motion with the obstacle density, while slow obstacle dynamics results in particle motion that is more singularly related to its free motion and preserves the negative differential mobility already seen at $γ=0$. In more general terms that we also illustrate using one-dimensional random walkers, the mobility transition is between the time-scales of the quasi-stationary regime and that of the fluid limit.

cond-mat.stat-mech↗

arXiv2013

Active Fluctuation Symmetries

In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary driven particle systems such as the open Kawasaki lattice gas and the zero range model. As a measure of time-symmetric dynamical activity we take the difference $(N_1 - N_L)/T$ in the number of particles entering or leaving the system at the left versus the right edge of the system over time $T$. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.

cond-mat.stat-mech↗

arXiv2013

The frenetic origin of negative differential response

The Green-Kubo formula for linear response coefficients gets modified when dealing with nonequilibrium dynamics. In particular negative differential conductivities are allowed to exist away from equilibrium. We give a unifying framework for such negative differential response in terms of the frenetic contribution in the nonequilibrium formula. It corresponds to a negative dependence of the escape rates and reactivities on the driving forces. Partial caging in state space and reduction of dynamical activity with increased driving cause the current to drop. These are time-symmetric kinetic effects that are believed to play a major role in the study of nonequilibria. We give various simple examples treating particle and energy transport, which all follow the same pattern in the dependence of the dynamical activity on the nonequilibrium driving, made visible from recently derived nonequilibrium response theory.

cond-mat.stat-mech↗

arXiv2013

Low temperature behavior of nonequilibrium multilevel systems

We give a low temperature formula for the stationary occupations in Markovian systems away from detailed balance. Two applications are discussed, one to determine the direction of the ratchet current and one on population inversion. Both can take advantage of low temperature to improve the gain and typical nonequilibrium features. The new formula brings to the foreground the importance of kinetic aspects in terms of reactivities for deciding the levels with highest occupation and thus gives a detailed quantitative meaning to Landauer's blowtorch theorem at low temperature.

cond-mat.stat-mech↗

arXiv2013

On the second fluctuation--dissipation theorem for nonequilibrium baths

Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation-dissipation theorem. We show what is the proper nonequilibrium extension, to be applied when the environment is itself active and driven. In particular we determine the effective Langevin dynamics of a probe from integrating out a steady nonequilibrium environment. The friction kernel picks up a frenetic contribution, i.e., involving the environment's dynamical activity, responsible for the breaking of the standard Einstein relation.

cond-mat.stat-mech↗

arXiv2013

Linear response in the nonequilibrium zero range process

We explore a number of explicit response formulae around the boundary driven zero range process to changes in the exit and entrance rates. In such a nonequilibrium regime kinetic (and not only thermodynamic) aspects make a difference in the response. Apart from a number of formal approaches, we illustrate a general decomposition of the linear response into entropic and frenetic contributions, the latter being realized from changes in the dynamical activity at the boundaries. In particular, in this way one obtains nonlinear modifications to the Green-Kubo relation. We end by bringing some general remarks about the situation where that nonequilibrium response remains given by the (equilibrium) Kubo formula such as for the density profile in the boundary driven Lorentz gas.

cond-mat.stat-mech↗

arXiv2013

Probing active forces via a fluctuation-dissipation relation: Application to living cells

We derive a new fluctuation-dissipation relation for non-equilibrium systems with long-term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be accessed. For a silica bead attached to the wall of a living cell, we identify a crossover time between thermally controlled fluctuations and those produced by the active forces. We show that the probe position is eventually slaved to the underlying random drive produced by the so-called active forces.

cond-mat.soft↗