Anomalous relaxation from a non-equilibrium steady state: An isothermal analog of the Mpemba effect

Abstract

The Mpemba effect denotes an anomalous relaxation phenomenon where a system initially at a hot temperature cools faster than a system that starts at a less elevated temperature. We introduce an isothermal analog of this effect for a system prepared in a non-equilibrium steady state that then relaxes towards equilibrium. Here, the driving strength, which determines the initial non-equilibrium steady state, takes the role of the temperature in the original version. As a paradigm, we consider a particle initially driven by a non-conservative force along a one-dimensional periodic potential. We show that for an asymmetric potential relaxation from a strongly driven initial state is faster than from a more weakly driven one at least for one of the two possible directions of driving. These results are first obtained through perturbation theory in the strength of the potential and then extended to potentials of arbitrary strength through topological arguments.

Mpemba effect in driven granular gases: role of distance measures

“…However, the effect is not limited to water and has been experimentally shown to exist in many other physical systems such as magnetic alloys [7], clathrate hydrates [8], polylactides [9], carbon nanotube resonators [10] and colloidal systems [11][12][13], thus suggesting that the Mpemba effect is a much more general anomalous relaxation phenomenon that can be studied in numerous physical systems. Theoretical studies on the Mpemba effect have focused on spin systems [14][15][16][17][18][19], systems undergoing phase transitions [17,20,21], Markovian systems with only a few states [22,23], systems of single particle diffusing in a potential [24][25][26][27], active systems [28], spin glasses [29], molecular gases in contact with a thermal reservoir [30][31][32][33], quantum systems [34] and granular systems [35][36][37][38][39][40][41].…”

Landau theory for the Mpemba effect through phase transitions

“…These include experimental observations of hot systems that undergo a phase transition before cold systems in non-water substances (Polymers 10 , Clathrate hydrates 11 ), as well as in other types of phase transitions (Magnetic transition in alloys 12 and various spin models [13][14][15][16][17] ), relaxation towards equilibrium without a phase transition that is non-monotonous in the initial temperature [18][19][20][21][22] and similar effects in relaxation towards a non-equilibrium steady states in driven molecular gas models [23][24][25][26][27][28] . It was also recently used to describe relaxations in which the non-monotonic characteristic is not in the initial temperature, but in some other parameter 29 .…”