Effective Confinement as Origin of the Equivalence of Kinetic Temperature and Fluctuation-Dissipation Ratio in a Dense Shear Driven Suspension

TL;DR

This paper demonstrates that in dense shear-driven suspensions, an effective confinement leads to the equivalence of kinetic temperature and fluctuation-dissipation ratio, supported by theoretical derivation and numerical validation.

Contribution

It introduces a novel approach linking effective confinement to fluctuation-dissipation relations in dense suspensions, with a derivation and numerical evidence.

Findings

Effective confinement explains the equivalence of kinetic temperature and fluctuation-dissipation ratio.

Numerical simulations show the correction term is negligible in moderately dense suspensions.

The approach connects theoretical derivation with practical numerical validation.

Abstract

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time-scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.