Large deviation statistics of non-equilibrium fluctuations in a sheared model-fluid

TL;DR

This paper investigates the large deviation statistics of shear stress in a one-dimensional model fluid, revealing phase-dependent effective temperatures and confirming fluctuation relations across different phases.

Contribution

It demonstrates the applicability of the Gallavotti-Cohen fluctuation theorem to a model fluid with complex phase behaviour and introduces an effective temperature derived from large deviation functions.

Findings

Gallavotti-Cohen fluctuation theorem holds across all phases.

Effective temperature varies with strain rate and phase.

Large deviation principle applies to local strain rate statistics.

Abstract

We analyse the statistics of the shear stress in a one dimensional \emph{model fluid}, that exhibits a rich phase behaviour akin to real complex fluids under shear. We show that the energy flux satisfies the Gallavotti-Cohen FT across all phases in the system. The theorem allows us to define an effective temperature which deviates considerably from the equilibrium temperature as the noise in the system increases. This deviation is negligible when the system size is small. The dependence of the effective temperature on the strain rate is phase-dependent. It doesn't vary much at the phase boundaries. The effective temperature can also be determined from the large deviation function of the energy flux. The local strain rate statistics obeys the large deviation principle and satisfies a fluctuation relation. It does not exhibit a distinct kink near zero strain rate because of inertia of the rotors in our system.