Consequences of the connection between nonlinear Fokker-Planck equations
and entropic forms are investigated. A particular emphasis is given to
the feature that different nonlinear Fokker-Planck equations can be
arranged into classes associated with the same entropic form and its
corresponding stationary state.
Through numerical integration, the time evolution of the solution
of nonlinear Fokker-Planck equations related to the Boltzmann-Gibbs
and Tsallis entropies are analyzed.
The time behavior in both stages, in a time much smaller than the
one required for reaching the stationary state, as well as
towards the relaxation to the stationary state, are of particular interest.
In the former case, by
using the concept of classes of nonlinear Fokker-Planck equations,
a rich variety of physical behavior may be found, with some curious
situations, like an anomalous diffusion within the
class related to the Boltzmann-Gibbs entropy, as well as a
normal diffusion within the class of equations related
to Tsallis’ entropy. In addition to that, the relaxation
towards the stationary state may present a behavior
different from most of the systems studied in the literature.
05.40.Fb Random walks and Levy flights 05.20.-y Classical statistical mechanics 05.40.Jc Brownian motion 05.10.Gg Stochastic analysis methods