Do strange kinetics imply unusual thermodynamics? art. no. 021107

We introduce a fractional Fokker-Planck equation (FFPE) for Levy flights in the presence of an external field. The equation is derived within the fram ework of the subordination of random processes which leads to Levy flights. It is shown that the coexistence of anomalous transport and a potential di splays a regular exponential relaxation toward the Boltzmann equilibrium di stribution. The properties of the Levy-flight FFPE derived here are compare d with earlier findings for a subdiffusive FFPE. The latter is characterize d by a nonexponential Mittag-Leffler relaxation to the Boltzmann distributi on. In both cases, which describe strange kinetics, the Boltzmann equilibri um is reached, and modifications of the Boltzmann thermodynamics are not re quired.