Far-from-Equilibrium Distribution from Near-Steady-State Work Fluctuations

TL;DR

This paper develops a new theoretical approach to approximate the distribution of nonequilibrium steady states by expanding around the fixed point of driven dynamics, successfully capturing shear thinning in simulations.

Contribution

It introduces a novel expansion method based on linearized driven dynamics to describe nonequilibrium distributions beyond near-equilibrium conditions.

Findings

First two expansion terms explain shear thinning at high shear rates.

Method accurately describes statistics of driven colloidal systems.

Approach extends Boltzmann distribution concepts to far-from-equilibrium regimes.

Abstract

A longstanding goal of nonequilibrium statistical mechanics has been to extend the conceptual power of the Boltzmann distribution to driven systems. We report some new progress towards this goal. Instead of writing the nonequilibrium steady-state distribution in terms of perturbations around thermal equilibrium, we start from the linearized driven dynamics of observables about their stable fixed point, and expand in the strength of the nonlinearities encountered during typical fluctuations away from the fixed point. The first terms in this expansion retain the simplicity of known expansions about equilibrium, but can correctly describe the statistics of a certain class of systems even under strong driving. We illustrate this approach by comparison with a numerical simulation of a sheared Brownian colloid, where we find that the first two terms in our expansion are sufficient to account for the shear thinning behavior at high shear rates.