Non-equilibrium memory effects: Granular fluids and beyond

¹ Física Teórica, Universidad de Sevilla - Apartado de Correos 1065, E-41080 Sevilla, Spain
² Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla - Virgen de África 7, E-41011 Sevilla, Spain

^(a) E-mail: prados@us.es (corresponding author)

Received: 24 July 2023
Accepted: 8 September 2023

Abstract

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.