Mpemba effect on non-equilibrium active Markov chains

TL;DR

This paper investigates the Mpemba effect in a non-equilibrium active Markov chain model, revealing how activity influences anomalous relaxation, including suppression, induction, and oscillatory behaviors, with implications for biological systems.

Contribution

It introduces a Markov chain model for active particles demonstrating the Mpemba effect and uncovers novel oscillatory relaxation phenomena due to broken detailed balance.

Findings

Activity can suppress or induce the Mpemba effect.

Oscillatory Mpemba effect with multiple crossing points.

Complex eigenvalues lead to oscillatory relaxation trajectories.

Abstract

We study the Mpemba effect on a non-equilibrium Markov chain that mimics the run and tumble motion of an active particle in a discrete energy landscape. The broken detailed balance, rendered by the activity, gives rise to a unique anomalous relaxation in the system which is distinctly different than the typical equilibrium systems. We observe that the activity can both suppress or induce the Mpemba effect. Furthermore, we report an oscillatory Mpemba effect where the relaxation trajectories, emanating from the hot and cold initial conditions, cross each other multiple times and this occurs due to the emergence of complex eigenvalues in the relaxation spectrum due to the activity. Our work reveals a possible pathway for studying the Mpemba effect in active living systems where broken detailed balance is crucial to achieve many biological functions.