论文标题
关于几何学在统计力学和热力学中的作用II：热力学观点
On the role of geometry in statistical mechanics and thermodynamics II: Thermodynamic perspective
论文作者
论文摘要
非平衡性可逆 - 反转耦合（通用）的一般方程式提供了介观的多尺度动力学结构，可确保平衡状态的出现。同样，将通用结构提升到迭代的cotangent束，称为速率通用，保证了生成平衡方法的矢量场的出现。此外，速率通用结构还扩展了Onsager的变异原理。通用结构中的最大（最大熵）原理成为速率通用结构中的onsager变异原理。在没有外力的情况下，速率熵是与熵产生密切相关的潜力。在不存在熵的外部力量的情况下，距离熵仍然存在。虽然一般时间演化结束时的熵会引起平衡热力学，但速率熵在速率通用时间演化结束时的熵会导致速率热力学。在本系列的第一篇论文中，通用和速率通用结构都被放入几何框架中。速率通用也被证明与Grad降低Boltzmann方程的层次结构分析有关。化学动力学和动力学理论提供了说明性的例子。我们介绍了化学动力学和玻尔兹曼动力学理论的速率通用扩展（以及因此，也是化学动力学的Onsager-onsaniational-Priminciphiperials）。
The General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provides structure of mesoscopic multiscale dynamics that guarantees emergence of equilibrium states. Similarly, a lift of the GENERIC structure to iterated cotangent bundles, called a rate GENERIC, guarantees emergence of the vector fields that generate the approach to equilibrium. Moreover, the rate GENERIC structure also extends Onsager's variational principle. The MaxEnt (Maximum Entropy) principle in the GENERIC structure becomes the Onsager variational principle in the rate GENERIC structure. In the absence of external forces, the rate entropy is a potential that is closely related to the entropy production. In the presence of external forces when the entropy does not exist, the rate entropy still exists. While the entropy at the conclusion of the GENERIC time evolution gives rise to equilibrium thermodynamics, the rate entropy at the conclusion of the rate GENERIC time evolution gives rise to rate thermodynamics. Both GENERIC and rate GENERIC structures are put into the geometrical framework in the first paper of this series. The rate GENERIC is also shown to be related to Grad's hierarchy analysis of reductions of the Boltzmann equation. Chemical kinetics and kinetic theory provide illustrative examples. We introduce rate GENERIC extensions (and thus also Onsager-variational-principle formulations) of both chemical kinetics and the Boltzmann kinetic theory.
