Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908745328492544 |
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| author | Trajanovski, Pece Petreska, Irina Gorska, Katarzyna Kocarev, Ljupco Sandev, Trifce |
| author_facet | Trajanovski, Pece Petreska, Irina Gorska, Katarzyna Kocarev, Ljupco Sandev, Trifce |
| contents | A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with three different forms of the memory kernel. To analyse the probability density function, we utilize the subordination approach. Subsequently, the corresponding continuous time random walk model is presented. Furthermore, we investigate the effects of the stochastic resetting on the dynamics of the process and we showed that in the long time limit the system approaches a nonequilibrium stationary state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting Trajanovski, Pece Petreska, Irina Gorska, Katarzyna Kocarev, Ljupco Sandev, Trifce Statistical Mechanics A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with three different forms of the memory kernel. To analyse the probability density function, we utilize the subordination approach. Subsequently, the corresponding continuous time random walk model is presented. Furthermore, we investigate the effects of the stochastic resetting on the dynamics of the process and we showed that in the long time limit the system approaches a nonequilibrium stationary state. |
| title | Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2502.18700 |