论文标题
环球戈班的熵：几何案例研究
Universal Gorban's Entropies: Geometric Case Study
论文作者
论文摘要
最近，A.N。 Gorban为具有详细或复杂平衡的任何线性或非线性反应网络提供了丰富的通用Lyapunov功能。构造算法的两个主要要素是反应的部分平衡和功能家族家族的凸封。这些新功能旨在解决有关线性动力学的Lyapunov函数（F-Divergences）富裕家族之间的差异的“神秘”，以及在热力学条件下非线性网络的Lyapunov功能有限的收集。缺乏例子不允许评估Gorban的熵与古典Boltzmann（Gibbs） - Shannon熵之间的差异，尽管它们的构造有明显的差异。在本文中，A.N。的结果简要审查了Gorban，并分析了这些功能，并比较了几种化学反应机制。分析了沿动力学轨迹的水平集和动力学。新的和经典的热力学Lyapunov函数之间最明显的差异远离部分平衡，而当某些快速基本反应接近平衡时，这种差异就下降并消失了部分平衡。
Recently, A.N. Gorban presented a rich family of universal Lyapunov functions for any linear or non-linear reaction network with detailed or complex balance. Two main elements of the construction algorithm are partial equilibria of reactions and convex envelopes of families of functions. These new functions aimed to resolve "the mystery" about the difference between the rich family of Lyapunov functions (f-divergences) for linear kinetics and a limited collection of Lyapunov functions for non-linear networks in thermodynamic conditions. The lack of examples did not allow to evaluate the difference between Gorban's entropies and the classical Boltzmann--Gibbs--Shannon entropy despite of obvious difference in their construction. In this paper, results of A.N. Gorban are briefly reviewed, and these functions are analysed and compared for several mechanisms of chemical reactions. The level sets and dynamics along the kinetic trajectories are analysed. The most pronounced difference between the new and classical thermodynamic Lyapunov functions was found far from the partial equilibria, whereas when some fast elementary reactions became close to equilibrium then this difference decreased and vanished in partial equilibria.
