Ergotropic Mpemba crossings in finite-dimensional quantum batteries

TL;DR

This paper investigates the quantum Mpemba effect in finite-dimensional quantum batteries, introducing ergotropic crossings, analyzing conditions for their occurrence, and exploring differences between Markovian and non-Markovian dynamics.

Contribution

It introduces the concept of ergotropic Mpemba crossings in quantum batteries, providing conditions for their occurrence and analyzing their physical origin and dynamics.

Findings

Ergotropic crossings depend on initial state coherence and energy.

Non-Markovian dynamics can produce multiple crossings.

In qubits, coherence is crucial for crossings; this does not hold for qutrits.

Abstract

The quantum Mpemba effect is a counterintuitive phenomenon in which a state initially farther from equilibrium relaxes more rapidly than one that starts nearer to equilibrium. In the context of finite-dimensional quantum batteries interacting with an environment, we introduce the notion of an ergotropic Mpemba crossing (EMC), defined by the intersection of ergotropy trajectories during the dynamics. For qubit batteries subjected to amplitude damping noise, we derive a condition for the occurrence of EMC in terms of the relative coherence of the initial states and fully characterize the region of state space that exhibits EMC with respect to a fixed reference state. Interestingly, our analysis reveals that under anisotropic Pauli noise, the emergence of EMC is jointly governed by the coherence and the energy of the initial states. To elucidate the physical origin of EMC, we decompose ergotropy into coherent and incoherent contributions and show that, in qubit systems, the coherent component plays a crucial role for EMC, an observation that strikingly does not extend to three-level batteries. Further, by extending our analysis to non-Markovian environments, we demonstrate that, unlike the Markovian case, non-Markovian dynamics can give rise to multiple Mpemba crossings, with the total number of crossings always being odd. Moreover, analyzing the connection between the EMC and the conventional state Mpemba effect reveals that, for qubits, an EMC necessarily entails a state Mpemba crossing while this correspondence breaks down for qutrits, where EMCs may arise without any state Mpemba crossing.