Generalized chapman-kolmogorov equation: A unifying approach to the description of anomalous transport in external fields
The generalized Chapman-Kolmogorov equation [V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973)] is discussed. It is demonstrated that this equation unifies recently proposed kinetic equations of fractional order that describe anomalous transport in external fields, as well as continuous time random walks. The conditions under which the individual models can be established are discussed.
Metzler
R
Department of Physics and School of Chemical Sciences, University of Illinois at Urbana-Champaign, 600 South Mathews, MC-712 24-6, Urbana, Illinois 61801, USA.