# Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals

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## Abstract

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## 1. Introduction

## 2. Free Oscillations of a Chain with Retarded Interactions between the Particles

- If:$$\mathrm{\Gamma}\left({\tau}_{1},\phantom{\rule{0.166667em}{0ex}}k\right)>0$$
- If there were such values of k for which:$$\mathrm{\Gamma}\left({\tau}_{1},k\right)<0,$$

## 3. Dynamics of Forced Oscillations of a Chain with Retarded Interactions

## 4. Results

- It was found that the retardation of interactions between particles leads to a radical restructuring of the dynamics of a one-dimensional harmonic chain. In particular, due to the retardation of interactions, stationary free oscillations in the chain are impossible.
- Since the presence of free oscillations with increasing amplitudes means the destruction of the chain, a criterion for the absence of growing oscillations in the system was obtained. This criterion is a condition for the stability of the chain.
- It was shown that, when a stable chain of particles with retarded interactions between them is immersed in an alternating external field, the system passes into a stationary state, which depends both on the properties of the system and on the characteristics of the external field. This stationary state was interpreted as a dynamic equilibrium between a chain and an external field.

- The phenomenon of irreversibility;
- The existence of a thermodynamic equilibrium.

- The field nature of the interaction between particles;
- The principle of causality.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Zakharov, A.Y.; Zakharov, M.A. Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals. *Quantum Rep.* **2021**, *3*, 724-730.
https://doi.org/10.3390/quantum3040045

**AMA Style**

Zakharov AY, Zakharov MA. Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals. *Quantum Reports*. 2021; 3(4):724-730.
https://doi.org/10.3390/quantum3040045

**Chicago/Turabian Style**

Zakharov, Anatoly Yu., and Maxim A. Zakharov. 2021. "Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals" *Quantum Reports* 3, no. 4: 724-730.
https://doi.org/10.3390/quantum3040045