Thermodynamics of the quantum Mpemba effect

TL;DR

This paper explores the quantum Mpemba effect through non-equilibrium thermodynamics, showing how quantum states can relax faster to equilibrium under certain transformations, revealing a genuine quantum version of the effect.

Contribution

It introduces a quantum thermodynamic framework for the Mpemba effect, demonstrating how unitary transformations can induce the effect and analyzing relaxation dynamics in quantum systems.

Findings

Exponential speedup to equilibrium occurs when transforming to a diagonal state in the energy basis.

A genuine quantum Mpemba effect is identified when the transformed state has higher nonequilibrium free energy.

Unitary transformations can always be constructed to produce the quantum Mpemba effect.

Abstract

We investigate the quantum Mpemba effect from the perspective of non-equilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a \textit{genuine} quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the non-equilibrium free energy and the irreversible entropy production in single and multi-qubit examples.