Tsallis Entropy and Anomalous Dispersion in Stochastic Hydrology

Abstract:

It is well known that classical Fickian (Brownian) dispersion maximizes the Boltzmann-Gibbs entropy. Recently the Tsallis q-entropy has been developed as an alternative to the classical entropy for systems in which entropy may be non-extensive. In stochastic hydrology the velocity is generally modeled as a random field. Alternatively, though rarely done, the macro scale dispersion tensor can be modeled as a random function since it can be considered as a function of the random velocity. We demonstrate how Fickian motion can be generalized so that the Tsallis entropy is maximized rather than the Boltzmann-Gibbs entropy. This generalization results simply from using a random dispersion coefficient, and we derive the distribution of this coefficient as a function of q for 1 < q < 3.