Nanoscale non-equilibrium dynamics and the fluctuation-dissipation relation in an ageing polymer glass

Response functions(1) and fluctuations(2) measured locally in complex materials should equally well characterize mesoscopic-scale dynamics. The fluctuation-dissipation relation (FDR) relates the two in equilibrium, a fact used regularly, for example, to infer mechanical properties of soft matter from the fluctuations in light scattering(3). In slowly evolving non-equilibrium systems, such as ageing spin(4-5) and structural glasses(6,7), sheared soft matter(8) and active matter(9), a form of FDR has been proposed in which an effective temperature(10), T-eff, replaces the usual temperature, and universal behaviour is found in mean-field models(10,11) and simulations(6-8,12). Thus far, only experiments on spin-glasses(13) and liquid crystals(14) have succeeded in accessing the strong-ageing regime, where T-eff > T and possible scaling behaviour are expected. Here we test these ideas through measurements of local dielectric response and polarization noise in an ageing structural glass, polyvinyl acetate. The relaxation-time spectrum, as measured by noise, is compressed, and by response, is stretched, relative to equilibrium, requiring an effective temperature with a scaling behaviour similar to that of certain mean-field spin-glass models.