O'Malley Daniel, Vesselinov Velimir V, Cushman John H
Computational Earth Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, Indiana 47907, USA and Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042143. doi: 10.1103/PhysRevE.91.042143. Epub 2015 Apr 29.
Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q entropy, which is nonadditive, was developed as an alternative to the classical entropy for systems which are nonergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. The distribution of this coefficient is derived as a function of q for 1<q<3. Applications to transport in porous media are considered.
布朗运动作为经典的扩散过程，使玻尔兹曼 - 吉布斯熵最大化。非可加性的Tsallis q熵是作为经典熵的替代物而发展起来的，用于非遍历系统。我们给出了布朗运动的一种推广形式，它使Tsallis熵而非玻尔兹曼 - 吉布斯熵最大化。这个过程由具有随机扩散系数的布朗测度驱动。该系数的分布是作为1<q<3时q的函数推导出来的。文中考虑了其在多孔介质输运中的应用。
