Glass formers (from superconductors and colloids to polymers and supercooled liquids) are perennially out of equilibrium in an experimental setting, due to their exceedingly slow dynamics. As a result, theory and experiment have followed essentially diverging paths: the former concentrating on the unreachable equilibrium state, the latter measuring aging response functions. Nowadays we know that aging is related to the growth of glassy domains. From the theoretical point of view, these domains can be measured in simulations in terms of a growing dynamical coherence length extracted from four-point microscopic spatial correlation functions. From the experimental side, several approaches based on macroscopic responses have been proposed [Yoh et al., Phys. Rev. Lett. 82 (1999) 438; Albert et al., Science 352 (2016) 1309], although their connection with the microscopic coherence length has never been established.

Here I show how to relate both approaches quantitatively in two ways. First, linear response functions based on the fluctuation-dissipation ratio provide a precise relation between finite sizes (simulations) and finite times (experiments). This allows us to compare theory with experiment without relying on uncontrollable extrapolations to infinite times or system sizes [Janus Collaboration, PNAS 114 (2017) 1838]. Second, I explain how one can use non-linear response functions to measure a macroscopic coherence length that matches the (microscopic) coherence length used in theoretical work  [Janus Collaboration, Phys. Rev. Lett. 118 (2017) 157202] . These results have been made possible by new spin-glass simulations on Janus II. This custom-built computer, dedicated to spin-glass simulations, allows us to perform high-precision computations in very large systems, with more than 4 million spins. This last point is crucial to reach large values of the coherence length without finite-size effects, so we can connect to the experimental regime.