Nonequilibrium fluctuation dissipation relations of interacting Brownian particles driven by shear

TL;DR

This paper investigates how the fluctuation dissipation theorem (FDT) is modified in colloidal suspensions under steady shear near the glass transition, revealing a ratio different from equilibrium and restoring FDT form at short times.

Contribution

It provides a detailed theoretical analysis of FDT violations under shear using mode coupling approximations and introduces a reformulation involving the Hermitian part of the Smoluchowski operator.

Findings

FDT is violated under shear at long times

A constant FDT ratio different from equilibrium is observed

FDT holds at short times

Abstract

We present a detailed analysis of the fluctuation dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.