# Paths towards equilibrium in molecular systems: a mesoscopic Mpemba-like effect in water

## TL;DR

This paper demonstrates through numerical simulations that water exhibits a Mpemba-like effect during non-equilibrium cooling, occurring without phase transitions and linked to initial energy distribution.

## Contribution

It provides the first numerical evidence of a Mpemba effect in water, showing it arises from non-equilibrium energy distributions rather than phase transitions.

## Key findings

- Mpemba effect observed in water via simulations
- Effect linked to initial energy equipartition absence
- No phase transition involved in the effect

## Abstract

The so-called Mpemba effect, i.e. the observation that the warmer of two otherwise identical systems cools faster when both are refrigerated in the same thermal reservoir, is a hotly debated topic in condensed mater physics and statistical mechanics. Although it has been found in several non-equilibrium model systems, its very existence in water, the system in which it has been historically reported, is still open to question. Here we show using numerical simulations that a Mpemba effect is indeed present in water. We find that the effect occurs when equipartition of energy is not present in the initial state. Interestingly, the effect is observed without the intervention of a phase transition, and it is therefore seen to be a purely non-equilibrium relaxation effect.