Gomez Ignacio S, da Costa Bruno G, Dos Santos Maike A F
Instituto de Física, Universidade Federal da Bahia, Rua Barao de Jeremoabo, Salvador-BA 40170-115, Brazil.
Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, BR 407, km 08, Petrolina 56314-520, Pernambuco, Brazil.
Entropy (Basel). 2019 Jun 14;21(6):590. doi: 10.3390/e21060590.
In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the -Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions ϕ for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker-Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements. Moreover, assuming a dynamics satisfying continuous majorization, the -Boltzmann theorem is obtained as a special case for ϕ ( x ) = x ln x .
在这项工作中，我们展示了如何利用连续分布中的优超概念来刻画混合、扩散和量子动力学以及玻尔兹曼定理。关键在于优超的定义允许选择广泛的凸函数ϕ来研究给定的动力学。通过选择合适的凸函数，混合动力学、广义福克 - 普朗克方程和量子演化被刻画为沿时间演化的优超有序链，稳态是最小元素。此外，假设一种满足连续优超的动力学，对于ϕ(x)=xlnx的情况，玻尔兹曼定理作为一个特殊情况被得到。
