Stokes–Einstein relations and the fluctuation-dissipation theorem in a supercooled colloidal fluid

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Abstract
The Stokes–Einstein (SE) relation is a form of the fluctuation-dissipation theorem (FDT), and relates the diffusion coefficient of colloidal particles to the viscosity via the thermal energy kBT. We study the diffusion coefficient and viscosity of concentrated hard-sphere colloidal model systems in the frequency domain. We show that for these metastable fluid systems strong deviations from the SE relation occur, contrary to predictions of mode coupling theory. Using the FDT, these deviations can be quantified by an effective temperature, Teff. The deviation Teff/T−1 exhibits power-law behavior over several decades in frequency.