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

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

5 pages, no figures

References in corpus (5)

• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy $pp$ and $p\bar{p}$ collisions
• Dynamical collisional energy loss and transport properties of on- and off-shell heavy quarks in vacuum and in the Quark Gluon Plasma
• Transport Equation for Small Systems and Nonadditive Entropy
• Relationship between nonlinearities and thermalization in classical open systems: The role of the interaction range

Cited by in corpus (9)

• Fractal derivatives, fractional derivatives and $q$-deformed calculus
• Dynamics in fractal spaces
• Comparative study of the heavy-quark dynamics with the Fokker-Planck Equation and the Plastino-Plastino Equation
• The Theory of Thermodynamic Relativity
• Non-extensive Boltzmann Transport Equation: the Relaxation Time Approximation and Beyond
• Jet Quenching of the Heavy Quarks in the Quark-Gluon Plasma and the Nonadditive Statistics
• Quasiparticles for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
• Dynamics of Cities
• Scale dependence of the q and T parameters of the Tsallis distribution in the process of jet fragmentation