Anomalous cooling and heating - the Mpemba effect and its inverse

TL;DR

This paper proposes a universal thermodynamic mechanism explaining the Mpemba effect and its inverse, predicting their occurrence in various systems through non-equilibrium thermodynamics and Markovian dynamics.

Contribution

It introduces a general theoretical framework for the Mpemba effect and predicts the inverse effect, expanding understanding beyond specific systems.

Findings

A sufficient condition for the Mpemba effect in Markovian systems

Prediction of the inverse Mpemba effect in heating processes

Potential observation of these effects in new physical systems

Abstract

Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon - the "Mpemba Effect" - is well known in water, and has recently been observed in other systems as well. However, there is no single generic mechanism that explains this counter-intuitive behavior. Using the theoretical framework of non-equilibrium thermodynamics, we present a widely applicable mechanism for this effect, derive a sufficient condition for its appearance in Markovian dynamics, and predict an inverse Mpemba effect in heating: under proper conditions, a cold system can heat up faster than the same system initiated at a higher temperature. Our results suggest that it should be possible to observe the Mpemba effect and its inverse in a variety of systems, where they have never been demonstrated before.