From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation
A. Deppman, Alireza Khalili Golmankhaneh, Eugenio Megías, Roman Pasechnik
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.
Topics & Concepts
Fokker–Planck equationPhysicsBoltzmann equationBoltzmann constantBoltzmann's entropy formulaStatistical physicsEntropy (arrow of time)Mathematical physicsQuantum mechanicsPartial differential equationStatistical Mechanics and EntropyAdvanced Thermodynamics and Statistical MechanicsQuantum Mechanics and Applications