论文标题
某些热力学系统的几何形状
The geometry of some thermodynamic systems
论文作者
论文摘要
在本文中，我们继续该计划在上一篇文章中启动，从几何学的角度探索了一类重要的热力学系统。为了模拟验证热力学两个定律的系统的时间演变，我们表明进化矢量场的概念足以适当地描述此类系统。我们的配方自然源于引入偏斜的括号，基于离散梯度的数值方法非常合适。此外，我们研究了相应的拉格朗日和哈密顿形式主义，讨论了衍生方程的基本原理。我们形式主义自然涵盖的一类重要的系统是组成的热力学系统，这些系统由至少两个热变量和其组件之间的热量进行了描述。}。
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of thermodynamics, we show that the notion of evolution vector field is adequate to appropriately describe such systems. Our formulation naturally arises from the introduction of a skew-symmetric bracket to which numerical methods based on discrete gradients fit nicely. Moreover, we study the corresponding Lagrangian and Hamiltonian formalism, discussing the fundamental principles from which the equations are derived. An important class of systems that is naturally covered by our formalism are composed thermodynamic systems, which are described by at least two thermal variables and exchange heat between its components.}.
