Out‐of‐Equilibrium Generalized Fluctuation–Dissipation Relations

Recent molecular dynamics simulations of glass-forming liquids revealed superdiffusive fluctuations associated with the position of a tracer particle (TP) driven by an external force. Such an anomalous response, whose mechanism remains elusive, has been observed up to now only in systems close to their glass transition, suggesting that this could be one of its hallmarks. Here, we show that the presence of superdiffusion is in actual fact much more general, provided that the system is crowded and geometrically confined. We present and solve analytically a minimal model consisting of a driven TP in a dense, crowded medium in which the motion of particles is mediated by the diffusion of packing defects, called vacancies. For such nonglass-forming systems, our analysis predicts a long-lived superdiffusion which ultimately crosses over to giant diffusive behavior. We find that this trait is present in confined geometries, for example long capillaries and stripes, and emerges as a universal response of crowded environments to an external force. These findings are confirmed by numerical simulations of systems as varied as lattice gases, dense liquids, and granular fluids.

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“…Hence, in virtue of Eqs. (14), (15), (16) and (17), the return probability F * t (0|e µ |e ν ) is given explicitly by its Laplace transform…”

Section: B Single-vacancy Problemmentioning

confidence: 99%

Geometry-Induced Superdiffusion in Driven Crowded Systems

et al. 2013

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“…In the linear response regime, a fundamental result is the fluctuationdissipation theorem, which relates system response and spontaneous fluctuations. Within the last years a great effort has been devoted to generalizations of this theorem to nonequilibrium situations [1][2][3][4], when the time reversal symmetry is broken, and also to elucidating the effects of the higher order contributions in the external perturbation [5][6][7][8][9][10][11]. From experimental perspective, theoretical understanding of the latter issues is of an utmost importance in several fields, such as active microrheology [12][13][14] and dynamics of nonequilibrium fluids [15,16].…”

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confidence: 99%

Microscopic Theory for Negative Differential Mobility in Crowded Environments

et al. 2014

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We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.PACS numbers: 05.40.Fb,83.10.Pp Introduction.-Quantifying the response of a complex system to an external force is one of the cornerstone problems of statistical mechanics. In the linear response regime, a fundamental result is the fluctuationdissipation theorem, which relates system response and spontaneous fluctuations. Within the last years a great effort has been devoted to generalizations of this theorem to nonequilibrium situations [1][2][3][4], when the time reversal symmetry is broken, and also to elucidating the effects of the higher order contributions in the external perturbation [5][6][7][8][9][10][11]. From experimental perspective, theoretical understanding of the latter issues is of an utmost importance in several fields, such as active microrheology [12][13][14] and dynamics of nonequilibrium fluids [15,16].A striking example of anomalous behavior beyond the linear regime is the negative response of a particle's velocity to an applied force, observed in diverse situations in which a particle subject to an external force F travels through a medium. The terminal drift velocity V (F ) attained by the driven particle is then a nonmonotonic function of the force: upon a gradual increase of F , the terminal drift velocity first grows as expected from linear response, reaches a peak value and eventually decreases. This means that the differential mobility of the driven particle becomes negative for F exceeding a certain threshold value. Such a counter-intuitive "getting more from pushing less" [17] behavior of the differential mobility (or of the differential conductivity) has been observed for a variety of physical systems and processes, e.g. for electron transfer in semiconductors at low temperatures [18][19][20][21], hopping processes in disordered media [22], transport of electrons in mixtures of atomic gases with reactive collisions [23], far-from-equilibrium quantum spin chains [24], some models of Brownian motors [25,26], soft matter colloidal particles [27], different nonequilibrium systems [17], and also for the kinetically constrained models of glass formers [28][29][30].Apart of these examples, negative differential mobility (NDM) has been observed in the minimal model of a driven lattice gas, which captures many essential features of the behavior in r...

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“…in colloidal suspensions. In this regime, both fluctuations of the probe that can not be described correctly if the medium is treated as a continuous bath and super-diffusion regimes have been reported [2][3][4][5][6] Within a broader context, modeling the response of a medium to a perturbation created by a tracer particle, biased by an external force, is a ubiquitous problem in physics, which has been the subject of a large number of theoretical works [7][8][9]. The resulting stochastic dynamics of the whole system is however a many-body problem which is difficult (or even impossible) to solve even in the simplest case when the particle-particle interactions are a mere hard-core.…”

Section: Introductionmentioning

confidence: 99%

“…For that reason, in most approaches the microscopic structure of the bath is not taken into account explicitly, and the response functions are determined instead by using some effective bath dynamics, modelled via Langevin or generalized Langevin [10] equations (see also Refs. [7][8][9]). While these approaches are rather efficient, they cannot account for the detailed correlations between the tracer particle and the fluctuating density profiles of the bath particles.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations and correlations of a driven tracer in a hard-core lattice gas

et al. 2013

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We consider a driven tracer particle (TP) in a bath of hard-core particles undergoing continuous exchanges with a reservoir. We develop an analytical framework which allows us to go beyond the standard force-velocity relation used for this minimal model of active microrheology and quantitatively analyze, for any density of the bath particles, the fluctuations of the TP position and their correlations with the occupation number of the bath particles. We obtain an exact Einstein-type relation which links these fluctuations in the absence of a driving force and the bath particles density profiles in the linear driving regime. For the one-dimensional case we also provide an approximate but very accurate explicit expression for the variance of the TP position and show that it can be a non-monotoneous function of the bath particles density: counter-intuitively, an increase of the density may increase the dispersion of the TP position. We show that this non trivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross-correlations quantified by our approach.

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Out‐of‐Equilibrium Generalized Fluctuation–Dissipation Relations

Cited by 9 publications

References 87 publications

Geometry-Induced Superdiffusion in Driven Crowded Systems

Geometry-Induced Superdiffusion in Driven Crowded Systems

Microscopic Theory for Negative Differential Mobility in Crowded Environments

Fluctuations and correlations of a driven tracer in a hard-core lattice gas

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