Hotter Can Cool Faster: New Insights Into Counterintuitive Physics

The counterintuitive phenomenon where a hotter substance can, under certain conditions, cool faster than a colder one, known as the Mpemba effect, continues to fascinate physicists and challenge conventional understanding of thermal dynamics. Hui Yu, from the Beijing National Laboratory for Condensed Matter Physics and the Institute of Physics, Chinese Academy of Sciences, and Shuo Liu, from the Institute for Advanced Study at Tsinghua University, alongside Shi-Xin Zhang and colleagues, explore this effect within the realm of quantum mechanics in their review, ‘Quantum Mpemba Effects from Symmetry Perspectives’. The work investigates the connection between the quantum Mpemba effect and the breaking and restoration of symmetry within closed quantum systems, utilising metrics such as entanglement asymmetry and charge variance to analyse the dynamics of these systems under both Hamiltonian evolution and random unitary circuits.

Recent investigations reveal a compelling focus on non-equilibrium dynamics within quantum many-body systems, demonstrating behaviours that deviate from traditional expectations of thermalisation, the process by which a system reaches a stable equilibrium state. Researchers actively explore Many-Body Localisation (MBL), a phenomenon where strong disorder, or randomness in the system’s energy landscape, inhibits thermalisation, leading to a persistent, localised phase where interactions prevent the system from reaching equilibrium. This contrasts with ergodic systems, which explore all accessible states given sufficient time, highlighting a fundamental tension between localisation and thermalisation as key organising principles.

Dynamical Quantum Phase Transitions (DQPTs) and the phenomenon of prethermalisation further complicate this picture, demonstrating that systems undergoing rapid changes do not necessarily evolve directly to equilibrium. Instead, they often exhibit transient states, appearing to settle into quasi-equilibrium before ultimately localising or thermalising, suggesting a hierarchical structure to relaxation processes. These findings challenge the conventional understanding of phase transitions, extending the concept to time-dependent dynamics, where transitions occur not in response to changes in temperature, but in response to changes in time itself. Analog gravity and quantum simulation represent a significant application of these theoretical insights, allowing researchers to utilise condensed matter systems to model phenomena such as cosmological phase transitions and even the behaviour of time crystals, materials exhibiting periodic structure in time rather than space.

The Kibble-Zurek mechanism provides a framework for understanding the formation of topological defects, stable irregularities in a material, during these transitions, offering potential insights into the early universe and the formation of cosmic structures. Out-of-Time-Order Correlations (OTOCs) emerge as a crucial diagnostic tool for characterising quantum chaos, the unpredictable behaviour arising from quantum mechanics, and the transition between thermal and localised phases. OTOCs quantify the sensitivity of a system to perturbations, providing a measure of the breakdown of predictability and linking quantum chaos to the failure of thermalisation. Investigations into quantum information dynamics and the behaviour of open quantum systems, which consider the impact of environmental interactions, further strengthen this connection.

Future research should prioritise the development of more robust theoretical frameworks for predicting and understanding the interplay between disorder, interactions, and non-equilibrium dynamics. Specifically, exploring the limits of MBL in realistic systems, where perfect disorder is rarely achieved, and characterising the role of many-body effects in prethermalisation, where interactions between multiple particles dominate, are crucial. Furthermore, extending the scope of quantum simulation to encompass more complex phenomena and developing novel methods for probing OTOCs in experimental settings will be essential, promising to unlock new insights into the fundamental laws governing the behaviour of matter.

Researchers actively investigate the quantum Mpemba effect (QME), the counterintuitive observation that, under certain conditions, a hot system can cool faster than a cold one, to understand symmetry breaking and restoration. They utilise metrics like entanglement asymmetry, a measure of the imbalance in quantum entanglement, and charge variance, a measure of the spread of electrical charge, to probe the underlying dynamics. Analysis focuses on the early and late-time evolution of these key quantities under both Hamiltonian evolution, describing the system’s time evolution according to the laws of quantum mechanics, and within the framework of random unitary circuits, a theoretical model used to simulate quantum systems. This provides a quantifiable link between symmetry and the observed cooling rates, potentially revealing new insights into the fundamental principles governing thermal behaviour. Current research actively seeks to refine the understanding of the QME by exploring the influence of various parameters, such as system size, initial state preparation, and the nature of interactions between particles.