AI 中文总结
研究流体-流体界面处密度演化，推导广义吉布斯-杜亥姆框架，纳入动力学贡献，建立热力学与力学统一联系，提出密度演化方程，极限情况下能恢复声速定义等重要方程。
AI 中文摘要
经典吉布斯-杜亥姆关系适用于准静态过程，忽略了动力学效应，导致吉布斯热力学与牛顿力学之间存在根本差距。在此，我们推导了一个纳入动力学贡献的广义吉布斯-杜亥姆框架，从而在经典热力学和牛顿力学之间建立了统一联系。基于此框架，我们提出了一个控制流体-流体界面处密度动力学的替代演化方程。在适当的极限情况下，所得密度演化方程自然恢复了声速定义、伯努利定律和范德瓦尔斯状态方程。
英文摘要
The classical Gibbs-Duhem relation applies to quasi-static processes and neglects kinetic effects, leaving a fundamental gap between Gibbs thermodynamics and Newtonian mechanics. Here, we derive a generalized Gibbs-Duhem framework that incorporates kinetic contributions, thereby establishing a unified connection between classical thermodynamics and Newtonian mechanics. Based on this framework, we propose an alternative evolution equation governing density dynamics at fluid-fluid interfaces. In appropriate limiting cases, the resulting density evolution equation naturally recovers the definition of the speed of sound, Bernoulli's law, and the van der Waals equation of state (EOS).
