Cooperative transport with selective kinetic constraints

Abstract

We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can be concave, convex or both, depending on the density of boundary particle reservoirs. A mean-field analysis based on a diffusion equation with a densitydependent diffusion coefficient qualitatively reproduces this behaviour, and suggests its occurrence in liquids with a diffusivity anomaly.

Casimir-like forces in cooperative exclusion processes

“…Although improved estimations can be obtained by using more refined expression of the diffusion coefficient with the systematic approaches developed in [24,25], we expect that corrections are rather mild. In particular, the prediction of the force sign and the location of the crossover between the attractive and repulsive regime should be quite accurate, as expected from numerical simulation of convexity-change profiles in the nonequilibrium steady state [30].…”

“…To estimate the diffusion coefficient of cooperative exclusion processes we use a mean-field argument which neglects particle correlations, according to which the average of the hopping probability, which is a certain function of multi-site occupancy variables, is approximated as a function of the average of the single site occupancy variable (i.e., the particle density ρ). This gives [30]:…”

“…where the binomial terms account for the multiplicity of possible configurations of particles and vacancies, that prevent hopping (with the power two coming from the detailed balance condition). This mean-field or no-correlation (NC) approximation provides a general upper bound on the actual diffusion coefficient and, although rather crude, it is surprinsingly good and versatile in predicting unsual convexity-change density profiles in boundary-driven nonequilibrium steady-states [30]. Moreover, for sufficiently large system size, transverse local density fluctuations are uncorrelated [30]:…”

“…and displays a maximum at ρ = 1/2. When coupled to particle reservoirs at its ends the model shows convexity-change profiles depending on the reservoirs density [30]. • S = {1}.…”

“…A direct inspection of figure 2 shows that the maximum of the repulsive force, which is attained at reservoir density ρ − 0.55, is twice as strong as the attractive force in the simple exclusion process (and equals in magnitude to the attractive force in the Kob-Andersen model). More importantly, the presence of a repulsive force can be inferred from the convexity properties of density profiles at different values of the density of boundary reservoirs [30], as suggested by the relation x (ρ) = D(ρ) (which follows from the expression of the steadystate current J = −D(ρ)∂ x ρ). This macroscopic static signature can be a useful diagnostic in the experimental or numerical investigation of model systems when a detailed knowledge of the bulk diffusion coefficient is lacking.…”