Zhen-Chuan (震川) Li (李)

By Zhen-Chuan Li

A variety of thermodynamic variables are properly arranged at vertices of an extended concentric multi-polyhedron diagram based on their physical meanings. A symmetric function with “patterned self-similarity” is precisely be defined as the function, which is unchanged not only in function form but also in variable’s nature and neighbor relationship under symmetric operations. Thermodynamic symmetry roots in the symmetric reversible Legendre transforms of the potentials. The specific thermodynamic symmetries revealed by the diagram are only one C3 symmetry about the U ∼ Φ diagonal direction and C4 and σ symmetries on three U-containing squares. Based on the equivalence principle of symmetry, numerous equations of the 12 families can concisely be depicted by overlapping 12 specifically created rigid, movable graphic patterns on fixed {1, 0, 0} diagrams through σ and/or C4 symmetric operations. Any desired partial derivatives can be derived in terms of several available quantities by a foolproof graphic method. It is the symmetry that made possible to build up the diagram as a model like the Periodic Table of the Elements to exhibit an integration of the entire structure of the thermodynamic variables into a coherent and complete exposition of thermodynamics and to facilitate the subject significantly.

Part of the book: Symmetry (Group Theory) and Mathematical Treatment in Chemistry