Nonequilibrium fluctuation dissipation relations of interacting Brownian particles driven by shear

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.

21 pages, 13 figures, submitted to Phys. Rev. E

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• The modified Sutherland--Einstein relation for diffusive nonequilibria
• Particle diode: Rectification of interacting Brownian ratchets
• Dynamical Heterogeneity in a Highly Supercooled Liquid under a Sheared Situation
• Mechanical Responses and Stress Fluctuations of a Supercooled Liquid in a Sheared Non-Equilibrium State
• From Equilibrium to Steady-State Dynamics after Switch-On of Shear
• Brownian systems perturbed by mild shear: Comparing response relations
• Tagged particle in a sheared suspension: effective temperature determines density distribution in a slowly varying external potential beyond linear response
• Non-Equilibrium relation between mobility and diffusivity of interacting Brownian particles under shear