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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16117 |
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Table of Contents:
- Non-equilibrium noise is characterized as noise realizations where external agitations disrupt the harmonic equilibrium of Brownian motion. Excitations in a particle's random walk into a so-called Lévy flight changes the distribution of the noise from Gaussian to the fat-tailed Lévy distribution. Generalization between Gaussian and Lévy distributions is the $α$-stability distribution, where $1<α\leq2$. In this study, the $α$-stability distributed noise is subjugated into the Langevin and fractional Fokker--Planck equations that correspond to a V-shaped linear potential well $V(x)=F|x|$. From these equations, an Euler scheme for computational simulation via iterations is presented, and a probability density function that is normalizable under any $α\in(1,2]$ is obtained. This study is focused more on the theoretical framework of non-equilibrium noise in V-shaped linear well profiles, which is intended to be applied to systems known to exhibit self-organized criticality.