# Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields

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## Abstract

**:**

## 1. Introduction

## 2. Theory and Results

#### 2.1. Onsager Reciprocal Relations and T-Symmetry

#### 2.2. Dynamics and Transformations

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

**Proposition**

**3.**

**Proof.**

#### 2.3. Gauge

**Proposition**

**4.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

#### 2.4. Magnetic field

**Proposition**

**5.**

**Proof.**

#### 2.5. Force Potentials

**Example**

**1.**

**Example**

**2.**

**Example**

**3.**

**Example**

**4.**

## 3. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Carbone, D.; Rondoni, L.
Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields. *Symmetry* **2020**, *12*, 1336.
https://doi.org/10.3390/sym12081336

**AMA Style**

Carbone D, Rondoni L.
Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields. *Symmetry*. 2020; 12(8):1336.
https://doi.org/10.3390/sym12081336

**Chicago/Turabian Style**

Carbone, Davide, and Lamberto Rondoni.
2020. "Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields" *Symmetry* 12, no. 8: 1336.
https://doi.org/10.3390/sym12081336