Slow dynamics and local quasi-equilibrium. Relaxation in supercooled colloidal systems

TL;DR

This paper develops a Fokker-Planck framework to describe slow relaxation in supercooled colloidal systems, introducing a local quasi-equilibrium assumption and a generalized Stokes-Einstein relation that aligns with experimental observations.

Contribution

It presents a novel non-Markovian Fokker-Planck equation based on local quasi-equilibrium, explaining anomalous diffusion behavior in supercooled colloids.

Findings

Derived a non-Markovian Fokker-Planck equation for supercooled colloids.

Introduced a generalized Stokes-Einstein relation with system temperature.

Explained experimental deviations from classical diffusion-viscosity proportionality.

Abstract

We present a Fokker-Planck description of supercooled colloidal systems exhibiting slow relaxation dynamics. By assuming the existence of a local quasi-equilibrium state during the relaxation of the system, we derive a non-Markovian Fokker-Planck equation for the non-stationary conditional probability. A generalized Stokes-Einstein relation containing the temperature of the system instead of the temperature of the bath is obtained. Our results explain experiments showing that the diffusion coefficient is not proportional to the inverse of the effective viscosity at frequencies related to the diffusion time scale.