Generalized fluctuation-dissipation relation and effective temperature in off-equilibrium colloids

The fluctuation-dissipation theorem (FDT), a fundamental result of equilibrium statistical physics, can be violated when a system is taken out of equilibrium. A generalization of FDT has been theoretically proposed for out-of-equilibrium systems; the kinetic temperature entering the fluctuation-dissipation relation (FDR) is substituted by a time-scale-dependent effective temperature. We combine the measurements of the correlation function of the rotational dynamics of colloidal particles obtained via dynamic light scattering with those of the birefringence response to study the generalized FDR in an off-equilibrium Laponite suspension undergoing aging. (i) We find that the FDT is strongly violated in the early stage of the aging process and is gradually recovered as the aging time increases and (ii) we determine the aging-time evolution of the effective temperature, comparing our results with those of previous experiments.