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

Airton Deppman; Alireza K. Golmankhaneh; Eugenio Megias; Roman Pasechnik

doi:10.1016/j.physletb.2023.137752

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arXiv · 2301.08500

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

Airton Deppman·Alireza K. Golmankhaneh·Eugenio Megias·Roman Pasechnik

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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 $q \rightarrow 1$ a smooth transition for the standard Fokker-Planck Equation is obtained.

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Airton Deppman, Alireza K. Golmankhaneh, Eugenio Megias, Roman Pasechnik. 2023-02-22. From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation. https://doi.org/10.1016/j.physletb.2023.137752

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