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

TL;DR

This paper demonstrates an isothermal analog of the Mpemba effect where a particle in a non-equilibrium steady state relaxes faster depending on initial driving strength, revealing a novel relaxation phenomenon.

Contribution

It introduces an isothermal analog of the Mpemba effect for non-equilibrium steady states and extends the analysis to arbitrary potential strengths using topological methods.

Findings

Faster relaxation from strongly driven states in asymmetric potentials.

Perturbation theory and topological arguments confirm the effect.

The effect depends on the direction of driving in the potential.

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.