# Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle

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## Abstract

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## 1. Introduction

## 2. Kinetic Interaction Principle and Master Equation

#### 2.1. Nonlinear Fokker–Planck Kinetics in One Dimension

#### 2.2. The Master Equation

#### 2.3. The Kinetic Interaction Principle

#### 2.4. Incoming and Outgoing Lattice Currents

#### 2.5. Continuity form of the Master Equation

## 3. The Nonlinear Fokker–Planck Current

#### 3.1. Lattice Expression of the Fokker–Planck Current

#### 3.2. Continuum Limit Expression of the Fokker–Planck Current

## 4. Fokker–Planck Equation and Discretization Schemes

#### 4.1. Temporal Discretization

#### 4.2. Linear Kinetics Regime

#### 4.3. Nonlinear Kinetics

## 5. Drift Current and Diffusion in Nonlinear Kinetics

#### 5.1. Nonlinear Drift and Fick Currents

#### 5.2. Nonlinear Kinetics with Fickian Diffusion

#### 5.3. The Case of Kappa Kinetics

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Kaniadakis, G.; Hristopulos, D.T.
Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle. *Entropy* **2018**, *20*, 426.
https://doi.org/10.3390/e20060426

**AMA Style**

Kaniadakis G, Hristopulos DT.
Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle. *Entropy*. 2018; 20(6):426.
https://doi.org/10.3390/e20060426

**Chicago/Turabian Style**

Kaniadakis, Giorgio, and Dionissios T. Hristopulos.
2018. "Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle" *Entropy* 20, no. 6: 426.
https://doi.org/10.3390/e20060426