Non-equilibrium memory effects: granular fluids and beyond

TL;DR

This paper explores memory effects in out-of-equilibrium systems, focusing on granular fluids and phenomena like Kovacs and Mpemba effects, highlighting their connection to control theory.

Contribution

It provides a perspective on memory effects in non-equilibrium systems, extending analysis to granular fluids and other contexts, and discusses their relation to optimal control.

Findings

Kovacs effect linked to imperfect steady state attainment

Mpemba effect involves faster reaching of steady state from further initial conditions

Connections to control theory suggest new ways to manipulate non-equilibrium systems

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