We present a Fokker-Planck description of supercooled colloidal systemsexhibiting slow relaxation dynamics. By assuming the existence of a localquasi-equilibrium state during the relaxation of the system, we derive anon-Markovian Fokker-Planck equation for the non-stationary conditionalprobability. A generalized Stokes-Einstein relation containing the temperatureof the system instead of the temperature of the bath is obtained. Our resultsexplain experiments showing that the diffusion coefficient is not proportionalto the inverse of the effective viscosity at frequencies related to thediffusion time scale.
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