Klika Václav, Pavelka Michal, Vágner Petr, Grmela Miroslav
Department of Mathematics-FNSPE, Czech Technical University, Trojanova 13, 12000 Prague, Czech Republic.
Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague, Czech Republic.
Entropy (Basel). 2019 Jul 22;21(7):715. doi: 10.3390/e21070715.
Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics.
任何物理系统都可以在不同的描述层次上进行考量，这些层次因描述的详细程度而异。我们提出了一种称为动态最大熵（DynMaxEnt）的方法，该方法提供了一条从更详细的演化方程到关于不太详细的状态变量的方程的途径。该方法基于对状态变量和共轭变量的明确识别，它们可以以不同方式趋向各自的准平衡态。详细的状态变量使用通常的最大熵原理（MaxEnt）进行约简，而共轭变量的弛豫保证了约简后的方程是封闭的。此外，可以构建一个连续的DynMaxEnt近似的无穷链。该方法在具有摩擦力的粒子、复杂流体（配备构象张量和雷诺应力张量）、双曲热传导和磁流体动力学中得到了验证。
