Nonequilibrium steady state and induced currents of a mesoscopically glassy system: Interplay of resistor-network theory and Sinai physics

Abstract

We introduce an explicit solution for the nonequilibrium steady state (NESS) of a ring that is coupled to a thermal bath, and is driven by an external hot source with log-wide distribution of couplings. Having time scales that stretch over several decades is similar to glassy systems. Consequently there is a wide range of driving intensities where the NESS is like that of a random walker in a biased Brownian landscape. We investigate the resulting statistics of the induced current I. For a single ring we discuss how sign of I fluctuates as the intensity of the driving is increased, while for an ensemble of rings we highlight the fingerprints of Sinai physics on the distribution of the absolute value of I.

Emergence of Sinai Physics in the stochastic motion of passive and active particles

“…In quasi-equilibrium conditions, under the influence of a bath that has uniform temperature, the system feature normal diffusion, while the extra transitions due to driving or propulsion mechanism lead to sub-diffusion and localization. This (and similar) counter-intuitive statements have been pointed out in some previous works in a way that was either blurred due to emphasis on related themes [17,18], or restricted to non-Brownian "runand-tumble particle" scenario [19,20] where the motion is frozen in the absence of propulsion (rather than diffusive). Also the strong relation between tight-binding chains and their continuum limit version has not been adequately clarified.…”

“…But for ν = 0 we expect a residual bias f (ν). The statistical properties of f (ν) has been studied in [17]. As in the benchmark Sinai model |f (ν)| ∼ f L .…”

Nonequilibrium version of the Einstein relation

“…In general the transition rates are random and asymmetric. In previous publications [7,8] we have highlighted the relevance of Sinai spreading [9] to the analysis of the induced v. Optionally one may have in mind the unfolded version of our ring. The latter concerns the motion of a Brownian particle in a tilted periodic array of identically disordered unit cells.…”

Emergence of Sinai physics in the stochastic motion of passive and active particles

“…The unbiased transition rates are w β = 1, the propulsion rate is ln(w ν ) = 1, and the flipping rate is w α = 2. The disorder parameters are σ v = 1 and σ = 0.1, as defined after equation (24). Panels (a) and (b) are for f = 10 −4 and f = 10 −2 , respectively, that are smaller and larger than f c .…”