Non-equilibrium memory effects: Granular fluids and beyond

In this perspective paper, we look into memory effects in out-of-equilibrium systems. To be concrete, we exemplify memory effects with the paradigmatic case of granular fluids, although extensions to other contexts such as molecular fluids with non-linear drag are also considered. The focus is put on two archetypal memory effects: the Kovacs and Mpemba effects. In brief, the first is related to imperfectly reaching a steady state —either equilibrium or non-equilibrium—, whereas the second is related to reaching a steady state faster despite starting further. Connections to optimal control theory thus naturally emerge and are briefly discussed.