Anomalous Brownian motion via linear FokkerPlanck equations
Abstract
According to a traditional point of view Boltzmann entropy is intimately related to linear FokkerPlanck equations (Smoluchowski, KleinKramers, and Rayleigh equations) that describe a wellknown nonequilibrium phenomenon: (normal) Brownian motion of a particle immersed in a thermal bath. Nevertheless, current researches have claimed that nonBoltzmann entropies (Tsallis and Renyi entropies, for instance) may give rise to anomalous Brownian motion through nonlinear FokkerPlanck equations. The novelty of the present article is to show that anomalous diffusion could be investigated within the framework of nonMarkovian linear FokkerPlanck equations. So on the ground of this nonMarkovian approach to Brownian motion, we find out anomalous diffusion characterized by the mean square displacement of a free particle and a harmonic oscillator in absence of inertial force as well as the mean square momentum of a free particle in presence of inertial force.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.02670
 Bibcode:
 2017arXiv170102670B
 Keywords:

 Physics  General Physics
 EPrint:
 Submitted. arXiv admin note: substantial text overlap with arXiv:1503.07951