Athermality and Asymmetry Explain Anomalous Relaxation, Including the Mpemba Effect

The counterintuitive observation that hot water can sometimes freeze faster than cold water, known as the Mpemba effect, has long puzzled scientists, and similar anomalous behaviours extend even beyond everyday thermal dynamics into more complex systems. Alessandro Summer, Mattia Moroder, and Laetitia Bettmann from Trinity College Dublin, along with colleagues including Xhek Turkeshi and Iman Marvian, now demonstrate a unifying principle underlying these seemingly disparate effects. Their work reveals that a concept from information theory, known as ‘resources’, provides a powerful framework for understanding both the conventional thermal Mpemba effect and its counterpart observed during symmetry restoration. By connecting these phenomena to the resources of athermality and asymmetry, the researchers uncover a shared dynamic, showing that the speed of thermalisation and symmetry change depends on the initial state’s relationship to the slowest relaxing modes within the system, offering a new perspective on how systems evolve towards equilibrium.

The Mpemba effect, originally observed as faster cooling of hotter samples, describes a counterintuitive phenomenon where, under certain conditions, a system initially at a higher temperature can cool more rapidly than one starting at a lower temperature. This effect has since been observed in various contexts, even extending to changes in symmetry within quantum systems. Recent research demonstrates that a powerful framework, known as ‘resource theory,’ provides a unifying explanation for these seemingly disparate instances of the Mpemba effect.

Symmetry, Thermalization and the Quantum Mpemba Effect

This work investigates how symmetries influence the behaviour of quantum systems as they interact with their environment and reach a stable state, known as thermalization. The research focuses on understanding how these symmetries impact the dynamics of open quantum systems, systems that exchange energy and information with their surroundings. The team explores how the interplay between a system and its environment dictates the speed at which it relaxes to equilibrium, and how this process can sometimes exhibit unexpected, non-monotonic behaviour like the Mpemba effect. The research builds on the concept of ‘resource theories’, a mathematical framework that identifies the essential properties needed to achieve specific transformations.

By quantifying these ‘resources’, scientists can better understand the underlying drivers of physical processes and predict how systems will evolve. The team demonstrates that the speed of equilibration is directly linked to the initial amount of these resources, with states possessing more resource dissipating it more rapidly and reaching equilibrium faster. The study reveals a crucial connection between global symmetries of the combined system and environment, and the resulting behaviour of the system alone. If the combined system-environment evolution respects a particular symmetry, and the environment is prepared in a symmetric state, then the resulting dynamics of the system will also exhibit that symmetry.

This connection provides a powerful tool for predicting and controlling the behaviour of open quantum systems. The research further explores the quantum Mpemba effect, where an initially non-equilibrium state can relax to equilibrium faster than a state closer to equilibrium. The team demonstrates that the presence and timing of this effect depend on the specific measure used to quantify the distance to equilibrium, highlighting the importance of choosing appropriate tools for analysing these complex dynamics.

Resource Theories Explain the Mpemba Effect

Researchers have developed a unifying framework for understanding the Mpemba effect by framing it within the concept of ‘resources’ in physics. This work demonstrates that the conventional thermal Mpemba effect arises from a resource called ‘athermality’, which measures a system’s deviation from thermal equilibrium. Interestingly, the Mpemba effect observed in symmetry restoration is governed by a resource related to asymmetry. This suggests a fundamental connection between these seemingly different phenomena, revealing a shared underlying mechanism. The research builds on the concept of ‘resource theories’, a mathematical framework used to define what transformations are possible under certain constraints.

By identifying which states require additional resources to create, scientists can better understand the underlying drivers of physical processes. The team demonstrates that the speed of equilibration is directly linked to the initial amount of these resources, with states possessing more resource dissipating it more rapidly and reaching equilibrium faster. Importantly, the team discovered a parallel between thermal and symmetry-related Mpemba effects. They found that the speed of symmetry restoration is determined by the initial overlap with the slowest symmetry-restoring mode, mirroring the role of the slowest decaying mode in the thermal Mpemba effect.

This suggests a fundamental connection between these seemingly different phenomena, revealing a shared underlying mechanism. The research further clarifies that system dynamics can be separated into components that either respect or break symmetry, providing a more nuanced understanding of how systems evolve. The implications of this work extend beyond a purely theoretical understanding of the Mpemba effect, potentially leading to applications in areas such as materials science and quantum computing.

Mpemba Effect Links Thermodynamics and Symmetry

This work demonstrates a unifying principle for understanding the Mpemba effect by framing it within the concept of resources in physics. The researchers show that the conventional thermal Mpemba effect arises from the resource of athermality, while the effect observed in symmetry restoration is linked to the resource of asymmetry. Importantly, they establish a parallel between these seemingly different phenomena, revealing that the dynamics of thermalization naturally separates into symmetry-respecting and symmetry-breaking components. The study highlights that the Mpemba effect in symmetry restoration is governed by the initial overlap with the slowest symmetry-restoring mode, mirroring the role of the slowest mode in thermal dynamics.

Using a model of an open quantum system, the researchers demonstrate that specific transformations can lead to exponentially faster thermalization, particularly for initial states possessing certain properties. The authors acknowledge that the quantification of the Mpemba effect can depend on the specific mathematical measure chosen, potentially leading to differing conclusions. Future research could explore the implications of these resource-theoretical insights for controlling and optimizing thermal processes in various physical systems. By framing the Mpemba effect within a resource-theoretic framework, researchers can now quantify the factors driving faster equilibration, opening avenues for manipulating these resources to control the speed of thermalization and symmetry restoration.