# A Minimal Mechanism for the Phase Transition-Driven Mpemba Effect in Systems with a Single Order Parameter

## TL;DR

This paper explains how a hotter system can cool faster than a cooler one during phase transitions, using a simple model and simulations.

## Contribution

A minimal, general mechanism for the phase transition-driven Mpemba effect using a single order parameter and Markovian dynamics.

## Key findings

- A hotter system can reach a stable low-temperature phase faster by avoiding energy barriers.
- The extended spin-1 Nagle–Kardar model demonstrates the Mpemba effect through Monte Carlo simulations.
- The initial state's position in order parameter space determines the kinetics of phase transitions.

## Abstract

The Mpemba effect, where a hotter system can enter a cold phase faster than a cooler one, remains a counterintuitive phenomenon whose origins are still being unraveled. In this work, we propose and demonstrate a simple and general mechanism for the genuine, phase transition-driven Mpemba effect. Our mechanism requires only a single order parameter to describe the system’s state and operates within a standard Markovian framework, distinguishing it from previous models that necessitate multiple order parameters or non-Markovian dynamics. The core of the effect lies in the distinct relaxation pathways following a sudden quench: a system prepared at a higher initial temperature may be projected onto a region of the final free-energy landscape that requires it to cross fewer energy barriers to reach the stable low-temperature phase, whereas a system prepared at an intermediate temperature may be trapped in a metastable state, requiring the crossing of multiple barriers. We concretely illustrate this mechanism using the extended spin-1 Nagle–Kardar model, where an appropriate choice of parameters yields the requisite free-energy topography. Through extensive Monte Carlo simulations, we confirm that the initially hot system consistently reaches the final ferromagnetic phase in less time than its initially warm counterpart, thereby exhibiting a robust Mpemba effect. Our findings provide a minimal and clear explanation for how the initial state’s position in order parameter space can dictate the kinetics of a first-order phase transition, leading to this anomalous acceleration of cooling.