Casas G A, Nobre F D, Curado E M F
Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061136. doi: 10.1103/PhysRevE.86.061136. Epub 2012 Dec 27.
The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.
分析了由非线性福克-普朗克方程描述的系统的熵时间率，这些方程与广义熵形式直接相关。研究了与不可逆过程相关的熵产生以及从系统到其周围环境的熵通量。考虑了一些已知广义熵形式的例子，特别是从线性福克-普朗克方程得到的玻尔兹曼-吉布斯熵的通量和产生作为特殊情况被恢复。由于非线性福克-普朗克方程适用于自然界中几种物理现象的动力学行为，比如复杂系统领域内的许多现象，所以本分析应适用于一大类非线性系统中的不可逆过程，例如由Tsallis熵和Kaniadakis熵描述的那些系统。
