Quantum Mpemba Effects from Symmetry Perspectives

TL;DR

This paper reviews the quantum Mpemba effect, highlighting its connection to symmetry breaking and restoration in quantum many-body systems, and introduces entanglement asymmetry and charge variance as key analytical tools.

Contribution

It provides a symmetry-based perspective on the quantum Mpemba effect and introduces new metrics for analyzing its dynamics in quantum systems.

Findings

Quantum Mpemba effect linked to symmetry dynamics.

Entanglement asymmetry and charge variance as probes.

Analysis of dynamics under Hamiltonian evolution and circuits.

Abstract

Non-equilibrium dynamics have become a central research focus, exemplified by the counterintuitive Mpemba effect where initially hotter systems can cool faster than colder ones. Studied extensively in both classical and quantum regimes, this phenomenon reveals diverse and complex behaviors across different systems. This review provides a concise overview of the quantum Mpemba effect (QME), specifically emphasizing its connection to symmetry breaking and restoration in closed quantum many-body systems. We begin by outlining the classical Mpemba effect and its quantum counterparts, summarizing key findings. Subsequently, we introduce entanglement asymmetry and charge variance as key metrics for probing the QME from symmetry perspectives. Leveraging these tools, we analyze the early- and late-time dynamics of these quantities under Hamiltonian evolution and random unitary circuits. We conclude by discussing significant challenges and promising avenues for future research.