From a mathematical point of view, thermodynamic properties behave like multi-variable functions and can usually be differentiated and integrated. An interpretation of thermodynamics being a science of symmetry was proposed by Herbert Callen, however such an abstract conceptual interpretation has not widely been recognized.Symmetry generally conveys two primary meanings: beauty and 'patterned self-similarity'. A symmetric function with 'patterned self-similarity' can precisely be defined as the function, which is unchanged not only in functional form but also in variable's nature and their relationship under symmetrical operations. The simplest and most evident symmetrical operations happen in the geometric symmetry of a physical object. Therefore it is possible to employ geometry to reveal symmetry in thermodynamics and incorporate the symmetry further to develop a coherent geometrical model in thermodynamics and facilitate the subject with the symmetry in the model.It took me more than fifty years gradually to do so: A variety of thermodynamic (totally forty four) variables for a one-phase single component system are properly arranged at vertices of an extended concentric multi-polyhedron  based on their physical meanings. Numerous (more than three hundreds) thermodynamic relationships can concisely be depicted by overlapping specific movable patterns on fixed diagrams through symmetrical operations. Many desired partial derivatives can visually be derived in terms of several measurable variables by a foolproof graphical method like getting destinations on a map.Thermodynamic symmetry roots in the Legendre transformations with 'patterned self-similarity'. It has been verified that the thermodynamic symmetry is not as perfect as the geometrical symmetry is since a special thermodynamic potential, F = F(T,P,�) = 0, damages the cube symmetry and that it is only one C3 symmetry about the special conjugate 'U~F' pair rather than four C3 symmetries in the cube and shows C4and s symmetries on three U-containing squares, where the U, H, G, and A square is most important and useful .

Symmetry in thermodynamics

247th National Meeting (2014)

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.