Asymmetric Exclusion Processes with Constrained Dynamics

Abstract

Asymmetric exclusion processes with locally reversible kinetic constraints are introduced to investigate the effect of non-conservative driving forces in athermal systems. At high density they generally exhibit rheological-like behavior, negative differential resistance, two-step structural relaxation, dynamical heterogeneity and, possibly, a jamming transition driven by the external field.There is a growing appreciation that glassy relaxation can be ascribed to purely dynamic restriction on the particle motion with static correlations and related thermodynamic factors playing little or no role [1,2,3]. Kinetically constrained models (KCMs) provide a simple and elegant way to rationalize this idea and have spurred the challenge to reproduce much of the observed glassy behavior [4], including detailed predictions that first originated in apparently unrelated and complementary meanfield approaches [5,6]. While investigations of KCMs have been mostly focused on equilibrium and aging dynamics, there are relatively few studies dealing with the effects of nonconservative forces. The issue is of special interest in rheology, where the apparent viscosity of structured liquids is found to depend on the applied stirring force [7]. Shear-thinning refers to the commonly observed situations in which the viscosity decreases at increasing forces, and is well described by mode-coupling theory [8]. The opposite, shear-thickening, behavior is less common and much more difficult to predict. In some cases the viscosity increase can be so dramatic that the macroscopic motion may even stop, the liquid jams [7,9]. It has been suggested that shear-thickening and jamming [10] are related to an underlying glass transition [11]. The idea has been interpreted microscopically in terms of an entropy-driven inverse freezing [12] and recent experiments have come to support this interpretation [13,14]. The latter approach, however, requires some special thermodynamic and structural features which are absent in athermal shear-thickening systems (e.g. concentrated suspensions of hard spheres). Accordingly, any attempt at unifying different types of dynamical arrest in systems dominated by steric hindrance and packing effects should explain the simultaneous emergence of thinning and thickening behavior with their underlying glassy dynamics.In this Letter I will show that rheological-like behavior occurs in microscopic models of finite dimensional particle systems interacting only through non-Hamiltonian forces and purely kinetic constraints. Evidence is provided by considering a variant of the asymmetric simple exclusion process (ASEP) [15], in which particle motion obeys an additional constraint motivated by lattice glass models [16]. Similarly to the ASEP the transition probabilities satisfy local detailed balance although, due to the periodic boundary condition, the driving field cannot be derived from a Hamiltonian. The applied field induces a nonequilibrium steady state (NESS) in the system. At small field the transport is ohmic and thinning ...

Dynamics of a homogeneous active dumbbell system

“…The non-monotonic dependence of χ(F act , φ) on F act for sufficiently large φ is reminiscent of -though not the same as -a negative resistivity, that is to say a decreasing dependence of a current on the applied field that drives it, observed, for instance, in sufficiently dense kinetically constrained systems [84]. We extract the slope of these time-dependent curves for times such that t t a and we call it dµ(F act , φ).…”

Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility

“…Just beyond this value, the differential mobility dµ/dF becomes negative, implying a slowing down of the particle motion at increasing force. This kind of phenomenon, denoted with the telling expression "getting more from pushing less", has been explained for nonequilibrium toy models in [18] and can be observed in different systems, such as Brownian motors [19], kinetically constrained models of glass formers [20,21] and driven lattice gases [22][23][24][25][26], where analytic approaches are possible [22,24,26]. In most of the aforementioned systems the non-linear behavior is due to a reciprocal tracer-medium interaction, i.e.…”

Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

“…This remarkable "getting more from pushing less" behavior [46] occurs not only in lattice models, but it is observed in several systems, such as nonequilibrium steady states [46], Brownian motors [47,48], and kinesin models [49]. In particular, in the context of kinetically constraint models, NDM has been observed in numerical simulations in [40,50] and related to the heterogeneity and intermittency of the dynamics in the glassy phase [40]. More recently, an analytical theory accounting for NDM in a Lorentz lattice gas, where the TP travels among fixed obstacles, has been presented by Leitmann and Franosch [41] in the dilute limit (i.e.…”