On the non-linear Fokker-Planck equation associated with kappa-entropy

Based on the method developed in [T.D. Frank, Physica A 310 397-412 (2002)], we have derived a non-linear Fokker-Planck equation for non-equilibrium systems related to the kappa-entropy. This kinetic equation can be characterized by the associated Lyapunov functional or Bregman type divergence, which is related to the difference of the kappa-generalized free-energies.