Out of equilibrium generalized Stokes-Einstein relation: determination of the effective temperature of an aging medium

TL;DR

This paper investigates how the anomalous motion of particles in aging media can be used to determine an effective temperature through a generalized Stokes-Einstein relation, combining experimental measurements with a simple power-law model.

Contribution

It introduces a method to extract the effective temperature of an aging medium from experimental data using a generalized Stokes-Einstein relation.

Findings

Effective temperature can be deduced from mean-square displacement and mobility measurements.

The approach is illustrated with a power-law model of aging media.

Provides a framework for analyzing out-of-equilibrium systems.

Abstract

We analyze in details how the anomalous drift and diffusion properties of a particle evolving in an aging medium can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility of a particle immersed in an aging medium such as a colloidal glass give access to an out of equilibrium generalized Stokes-Einstein relation, from which the effective temperature of the medium can eventually be deduced. We illustrate the procedure on a simple model with power-law behaviours.