Quantum and classical ergotropy from relative entropies

TL;DR

This paper explores the concepts of quantum and classical ergotropy, introducing a unified geometric framework using relative entropies to quantify work extraction from quantum and classical states, with applications to thermal states.

Contribution

It introduces the classical ergotropy concept and a geometric relative entropy framework to unify quantum and classical work extraction analysis.

Findings

Defined classical ergotropy for inhomogeneous energy distributions

Established a geometric approach to relative entropy in quantum mechanics

Applied the framework to conditional thermal states and refined the maximum work theorem

Abstract

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.