Title: Anomalous Brownian motion via linear Fokker-Planck equations,
Abstract: According to a traditional point of view Boltzmann entropy is intimately
related to linear Fokker-Planck equations (Smoluchowski, Klein-Kramers, and
Rayleigh equations) that describe a well-known nonequilibrium phenomenon:
(normal) Brownian motion of a particle immersed in a thermal bath.
Nevertheless, current researches have claimed that non-Boltzmann entropies
(Tsallis and Renyi entropies, for instance) may give rise to anomalous Brownian
motion through nonlinear Fokker-Planck equations. The novelty of the present
article is to show that anomalous diffusion could be investigated within the
framework of non-Markovian linear Fokker-Planck equations. So on the ground of
this non-Markovian 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.