2000/11/03 by Igor M. Sokolov, I. M. Sokolov, J. Klafter +2 · 1 citation
Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Advanced Thermodynamics and Statistical Mechanics #Crime, Illicit Activities, and Governance #Fractional Differential Equations Solutions #Poisoning and overdose treatments #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.64.021107
published as Phys. Rev. E, v. 64, art. no. 021107 (2001)
arxiv created 2000/11/03 · openalex publication_date 2007/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/28
We introduce a fractional Fokker-Planck equation (FFPE) for Lévy flights in the presence of an external field. The equation is derived within the framework of the subordination of random processes which leads to Lévy flights. It is shown that the coexistence of anomalous transport and a potential displays a regular exponential relaxation toward the Boltzmann equilibrium distribution. The properties of the Lévy-flight FFPE derived here are compared with earlier findings for a subdiffusive FFPE. The latter is characterized by a nonexponential Mittag-Leffler relaxation to the Boltzmann distribution. In both cases, which describe strange kinetics, the Boltzmann equilibrium is reached, and modifications of the Boltzmann thermodynamics are not required.