# Stochastic Thermodynamics of Oscillators’ Networks

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## Abstract

**:**

## 1. Introduction

## 2. Hamiltonian-Lagrange Formulation for Complex Equations of Motion

## 3. Fokker-Planck Equation and Entropy Production

## 4. Transported Vs Dissipated Heat

## 5. Application to Physical Systems

#### 5.1. Hamilton-Lagrange Description of a One Dimensional Continuum Ferromagnet

#### 5.2. Entropy Production for a Network of Classical Spins

#### 5.3. Entropy Production in the Frenkel-Kontorova Model

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Magnetisation vector M precessing around the effective field H along the z direction. The precession occurs in the x-y plane and is conveniently described by the stereographic projection $\psi $. (

**b**) Network of nonlinear oscillators connected to thermochemical baths with different temperatures and chemical potentials. The “particle” current ${j}_{mn}^{p}$ describe the transport of the local power ${p}_{m}$ between oscillators m and n.

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Borlenghi, S.; Delin, A.
Stochastic Thermodynamics of Oscillators’ Networks. *Entropy* **2018**, *20*, 992.
https://doi.org/10.3390/e20120992

**AMA Style**

Borlenghi S, Delin A.
Stochastic Thermodynamics of Oscillators’ Networks. *Entropy*. 2018; 20(12):992.
https://doi.org/10.3390/e20120992

**Chicago/Turabian Style**

Borlenghi, Simone, and Anna Delin.
2018. "Stochastic Thermodynamics of Oscillators’ Networks" *Entropy* 20, no. 12: 992.
https://doi.org/10.3390/e20120992