本文研究可逆过程热力学的几何理论.由态空间Ω=∞~f态(f——自由度)的簇性结构分析,得到热力学第一、二定律的不变式,并用以分析低温逼近现象和第三定律.也得到一个对金相学有重要用途的镶加原理,可导致四元系的总相图,将对热力学的研究与应用,可能有所助益. In this paper, we study the geometric theory of thermodynamics of reversible processes.We derive the invariant of the first and second laws of thermodynamics from the cluster structure analysis of Ω = ∞ ~ f state (f-degree of freedom) in the state space, The third law, but also to get an inlay principle that has an important use for metallography, can lead to a general phase diagram of the quaternion that would be of help in the study and application of thermodynamics.