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

The fluctuation-dissipation relation (FDR), a fundamental result of equilibrium statistical physics, ceases to be valid when a system is taken out of the equilibrium. A generalization of FDR has been theoretically proposed for out-of-equilibrium systems: the kinetic temperature entering 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 clay suspension undergoing aging. We i) find that FDR 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, giving support to the proposed generalization scheme.