Approximate second laws and energy extraction from quantum batteries

TL;DR

This paper develops a framework for approximate thermal operations accounting for system perturbations, revealing how such disturbances enable finite energy extraction from quantum batteries, unlike ideal conditions.

Contribution

It introduces approximate second laws under perturbed thermal operations, showing how perturbations enable finite ergotropy extraction from quantum batteries.

Findings

Perturbations cause off-diagonal and diagonal state elements to interact.

Approximate thermal operations allow finite energy extraction from quantum batteries.

State transformation conditions are extended to include disturbances.

Abstract

Conservation of energy under thermal operations, \textbf{TO}, is ensured by commutation of the unitary generating such operations with the total Hamiltonian. However in realistic scenarios, perturbations or disturbances in the system are unavoidable, which in turn may alter the commutation relation and hence in succession may affect the physical processes governed by \textbf{TO}. We call the altered set of operations as approximate thermal operations, \textbf{TO}$_\epsilon$, where $\epsilon$ denotes a degree of disturbance. We provide state transformation conditions under such operations, providing what can be referred to as approximate second laws. We show that in presence of feeble perturbations in the system's Hamiltonian, the states transform in such a way that diagonal elements of the system states start talking not only with each other but also with the off-diagonal elements. In parallel, the off-diagonal elements transform in a way such that they start connecting with diagonal elements and other off-diagonal elements. Such cross-talk is disallowed in the unperturbed second laws. As an application, we show that approximate thermal operations may lead to finite ergotropy extraction from quantum batteries, something that the exact ones are unable to.