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

## TL;DR

This paper introduces a numerical method to reconstruct non-stationary memory kernels from experimental or simulation data, enabling better understanding of non-equilibrium dynamics in coarse-grained systems.

## Contribution

The authors develop a series expansion approach to compute time-dependent memory kernels from two-time correlation functions, applicable to non-stationary systems.

## Key findings

- Memory kernel duration exceeds particle attachment timescales in crystallization.
- Method successfully applied to Lennard-Jones melt crystallization.
- Provides insights into non-Markovian effects in out-of-equilibrium processes.

## Abstract

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