Fluctuation-dissipation relation in a colloidal glass : frequency and aging time dependence

We present an experimental and theoretical investigation of the Generalized Einstein Relation (GER), a particular form of a fluctuation-dissipation relation, in an out-of-equilibrium complex fluid. Micrometer beads, used as thermometers, are immersed in an aging colloidal glass to provide both fluctuation and dissipation measurements. The deviations from the Generalized Einstein Relation – GER ratio and effective temperature – are derived as a function of frequency and aging time. We interpret the observed deviations from GER as directly related to the evolution of relaxation times of the glass with aging time. In accordance with our previous results, deviations are only observed in the regime where the observation time scale is of the order of a characteristic relaxation time of the glass. Our scenario is confirmed by measurements of the GER ratio in a wide range of frequencies, at long aging times. PACS. 64.70.Pf Glass transitions – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 05.70.-a Thermodynamics