Anomalous discharging of quantum batteries: the ergotropic Mpemba effect

TL;DR

This paper uncovers a quantum version of the Mpemba effect in quantum batteries, showing that higher charged states can discharge faster, with analysis based on phase space relative entropy and Gaussian operations.

Contribution

It introduces a novel quantum Mpemba effect in quantum batteries and provides an analytical framework using phase space relative entropy to understand this phenomenon.

Findings

Higher charge states can discharge faster than lower ones.

Discharged rates vary for batteries charged to the same level with different operations.

Analytical expressions for ergotropy under dissipative dynamics are derived.

Abstract

Anomalous thermal relaxation is ubiquitous in nonequilibrium statistical mechanics. An emblematic example of this is the Mpemba effect, where an initially ``hot'' system cools faster than an initially ``cooler'' one. This effect has recently been studied in a variety of different classical and quantum settings. In this Letter, we find a novel signature of the Mpemba effect in the context of quantum batteries. We identify situations where batteries in higher charge states can discharge faster than less charged states. Specifically, we consider a quantum battery encoded in a single bosonic mode that is charged using unitary Gaussian operations. We show that the ergotropy, used here as a dynamical indicator of the energy stored in the battery, can be recast as a phase space relative entropy between the system's state and the unitarily connected passive state, at each time. Our formalism allows us to compute the ergotropy analytically under dissipative dynamics and allows us to understand the conditions which give rise to a Mpemba effect. We also find situations where two batteries charged to the same value using different operations can discharge at different rates.