Symmetry of the Linearized Boltzmann Equation II
Symmetry of the Linearized Boltzmann Equation II
复制标题
线性玻尔兹曼方程 II 的对称性
DOI：
10.1007/s10955-009-9805-2
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发表时间：
2009
影响因子：
1.6
通讯作者：
S. Takata
中科院分区：
文献类型：
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作者：
S. Takata
这是作者对线性化玻尔兹曼方程的对称性研究的第二部分。本部分的问题是稳定非平衡系统中的熵产生和 Onsager-Casimir 互易关系。在讨论了非平衡气体系统中的熵、熵流和熵产生的定义后，给出了稳态下熵产生的表达式。然后，对于均匀平衡状态弱扰动的系统，熵产生可以用线性玻尔兹曼方程的解来表示。热力学力和通量以及动力学系数仅根据熵产生的表达式来定义。传统类型的 Onsager-Casimir 关系被证明适用于有界域和无界域系统中克努森数的整个范围，前提是远场中的气体状态是满足后者玻尔兹曼方程的局部麦克斯韦状态。对于其他无界域系统，非常规互易性被证明成立。
This is the second part of the study by the author on the symmetry of the linearized Boltzmann equation. The issue of the present part is the entropy production and the Onsager–Casimir reciprocity relation in the steady non-equilibrium systems. After the discussions on the definition of the entropy, entropy flow, and entropy production in the non-equilibrium gas systems, the expression of the entropy production in the steady state is presented. Then, for the systems weakly perturbed from a uniform equilibrium state, the entropy production is shown to be expressed in terms of the solution of the linearized Boltzmann equation. The thermodynamic forces and fluxes and the kinetic coefficients are defined solely from the expression of the entropy production. The conventional-type Onsager–Casimir relation is shown to hold for the entire range of the Knudsen number in bounded- and unbounded-domain systems, provided that the state of the gas in a far field is a local Maxwellian satisfying the Boltzmann equation for the latter. As to the other unbounded-domain systems, a nonconventional reciprocity is shown to hold.