论文标题
汉密尔顿 - 雅各比热力学转化方法
Hamilton-Jacobi approach to thermodynamic transformations
论文作者
论文摘要
在本说明中，我们制定并研究了一种描述热力学转化的汉密尔顿 - 雅各比方法。热力学相空间假定接触歧管的结构，该点代表平衡状态仅限于该相空间的某些亚体。我们证明，汉密尔顿 - 雅各比理论一致地描述了在外部可控参数空间或等效的平衡状态空间上的热力学转变。事实证明，在汉密尔顿 - 雅各比（Hamilton-Jacobi）的描述中，主函数的选择不是唯一的，但是，对于给定转换的产生动力描述仍然与此选择相同。讨论了一些涉及理想气体热力学转化的示例，其中在平衡状态空间上的特征曲线完全描述了动力学。在热力学的背景下，还讨论了最近出现的几何汉密尔顿 - 雅各比制剂。
In this note, we formulate and study a Hamilton-Jacobi approach for describing thermodynamic transformations. The thermodynamic phase space assumes the structure of a contact manifold with the points representing equilibrium states being restricted to certain submanifolds of this phase space. We demonstrate that Hamilton-Jacobi theory consistently describes thermodynamic transformations on the space of externally controllable parameters or equivalently, the space of equilibrium states. It turns out that in the Hamilton-Jacobi description, the choice of the principal function is not unique but, the resultant dynamical description for a given transformation remains the same irrespective of this choice. Some examples involving thermodynamic transformations of the ideal gas are discussed where the characteristic curves on the space of equilibrium states completely describe the dynamics. The geometric Hamilton-Jacobi formulation which has emerged recently is also discussed in the context of thermodynamics.
