# Quantum and Classical Ergotropy from Relative Entropies

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## Abstract

**:**

## 1. Introduction

## 2. Quantum Ergotropy

## 3. Ergotropy from Quantum Coherence

## 4. Classical Ergotropy from Inhomogeneity

## 5. Ergotropy in Geometric Quantum Mechanics

## 6. Ergotropy from Conditional Thermal States

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Proof of Equation (5)

**Proof**

**of**

**Equation (5).**

## Appendix B. Proof of Equation (7)

**Proof**

**of**

**Equation (7).**

## Appendix C. Non-Negativity of Divergence-like Quantity in Thermodynamic Scenario

## Appendix D. Proof of Equation (19)

**Proof**

**of**

**Equation (19).**

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**MDPI and ACS Style**

Sone, A.; Deffner, S.
Quantum and Classical Ergotropy from Relative Entropies. *Entropy* **2021**, *23*, 1107.
https://doi.org/10.3390/e23091107

**AMA Style**

Sone A, Deffner S.
Quantum and Classical Ergotropy from Relative Entropies. *Entropy*. 2021; 23(9):1107.
https://doi.org/10.3390/e23091107

**Chicago/Turabian Style**

Sone, Akira, and Sebastian Deffner.
2021. "Quantum and Classical Ergotropy from Relative Entropies" *Entropy* 23, no. 9: 1107.
https://doi.org/10.3390/e23091107