From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation

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Deppman A., Khalili Golmankhaneh A., Megías E., Pasechnik R.

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol.839, 2023 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 839
• Publication Date: 2023
• Doi Number: 10.1016/j.physletb.2023.137752
• Journal Name: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Chemical Abstracts Core, INSPEC, zbMATH, Directory of Open Access Journals
• Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this work, we study the formal connections between the non-linear Fokker-Planck Equation associated with the non-additive entropy and the Boltzmann Equation with the non-additive correlation functional. The collisional term following the q-algebra is adopted. In the derivation of the non-additive Fokker-Planck Equation, two constraints are imposed on the final result: i) that the entropic index q is a characteristic parameter of the non-additive systems with a value that does not change with time, and ii) that for q→1 a smooth transition for the standard Fokker-Planck Equation is obtained.