# Control of Strongly Nonequilibrium Coherently Correlated States and Superconducting Transition Temperature

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## Abstract

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## 1. Introduction

## 2. On the Vlasov Kinetic Equations in Systems with Varying Internal Structure

#### 2.1. Averaging over all Tangent Spaces, Averaging over Speeds and accelerations of All Orders

#### 2.2. Averaging over Tangent Spaces of Accelerations of all Orders

- when there are no external forces in the system and no flow in the phase space ${P}_{S}=0$ (this case corresponds to complete equilibrium in the system);
- when external forces do not act directly in the system, but the flow of energy, particles or entropy is constant in the phase space ${P}_{S}=const$ (this corresponds to a strong deviation from equilibrium).

#### 2.3. Averaging over Tangent Spaces of Higher-Order Accelerations

## 3. On the Thermodynamics of Coherent-Correlated States of Complex Systems

## 4. Induced Acoustic Plasma Oscillations in Semiconductors in Coherently Correlated States and the Superconducting Transition Temperature

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dependence of the distribution function ${F}_{q}\left(\epsilon /T\right)$ on energy $\epsilon /T$ and coherence parameters $q<1$. With increasing deviation from equilibrium, there is an increase in localization. (The function values are represented in one color, and the zero value is represented in blue. The surface rises above the zero value.)

**Figure 2.**Dependence of the distribution function ${F}_{q}\left(\epsilon /T\right)$ on energy $\epsilon /T$ and coherence parameter $q>1$. With increasing deviation from equilibrium, there is an increase in delocalization. (Non-zero function values are represented in a single color, and a zero value is represented in blue. The surface rises above the zero value.)

**Figure 3.**Dependence ${k}_{{A}_{Q}}\left(q\right)$ in the expression for the number of particles. When $q=1.4$ there is a singularity.

**Figure 4.**Dependence of the average velocity ${u}_{eff}^{}\left(q\right)=\u2329u\left(q\right)\u232a$ on the nonequilibrium parameter q.

**Figure 5.**Dispersion of longitudinal vibrations in the jelly model for different nonequilibrium parameters. Above is a straight line corresponding to the equilibrium case, and below are curves for the values $\frac{{k}_{eff}^{}\left(q\right)}{{k}_{D}}=0.1,\hspace{0.17em}\hspace{0.17em}0.6,\hspace{0.17em}\hspace{0.17em}1.2$, respectively.

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**MDPI and ACS Style**

Kruchinin, S.P.; Eglitis, R.I.; Novikov, V.E.; Oleś, A.M.; Wirth, S.
Control of Strongly Nonequilibrium Coherently Correlated States and Superconducting Transition Temperature. *Symmetry* **2023**, *15*, 1732.
https://doi.org/10.3390/sym15091732

**AMA Style**

Kruchinin SP, Eglitis RI, Novikov VE, Oleś AM, Wirth S.
Control of Strongly Nonequilibrium Coherently Correlated States and Superconducting Transition Temperature. *Symmetry*. 2023; 15(9):1732.
https://doi.org/10.3390/sym15091732

**Chicago/Turabian Style**

Kruchinin, Sergei P., Roberts I. Eglitis, Valery E. Novikov, Andrzej M. Oleś, and Steffen Wirth.
2023. "Control of Strongly Nonequilibrium Coherently Correlated States and Superconducting Transition Temperature" *Symmetry* 15, no. 9: 1732.
https://doi.org/10.3390/sym15091732