Slow dynamics and local quasi-equilibrium—relaxation in supercooled colloidalsystems

Abstract

We present a Fokker–Planck description of supercooled colloidal systems exhibiting slowrelaxation dynamics. Assuming the existence of a local quasi-equilibrium state during therelaxation of the system, we derive a non-Markovian Fokker–Planck equation for thenon-stationary conditional probability. A generalized Stokes–Einstein relation containingthe temperature of the system at local quasi-equilibrium instead of the temperature of thebath is obtained. Our results explain experiments showing that the diffusion coefficient isnot proportional to the inverse of the effective viscosity at frequencies related to thediffusion timescale.