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We present a numerical method to compute non-equilibrium memory kernels basedon experimental data or molecular dynamics simulations. The procedure uses arecasting of the non-stationary generalized Langevin equation, in which weexpand the memory kernel in a series that can be reconstructed iteratively.Each term in the series can be computed based solely on knowledge of thetwo-time auto-correlation function of the observable of interest. As a proof ofprinciple, we apply the method to crystallization from a super-cooled LennardJones melt. We analyze the nucleation and growth dynamics of crystallites andobserve that the memory kernel has a time extent that is about one order ofmagnitude larger than the typical timescale needed for a particle to beattached to the crystallite in the growth regime.

Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables