Metric geometry of equilibrium thermodynamics. III. Elementary formal structure of a vector-algebraic representation of equilibrium thermodynamics

Publisher Website
Google Scholar
Abstract
The thermodynamic geometry established in an earlier paper is taken as the basis for an abstract vector-algebraic representation of equilibrium thermodynamics. In this representation, thermodynamic field variables appear as abstract Euclidean vectors whose lengths and internal angles describe the equilibrium properties. A variety of thermodynamic indentities, stability conditions, and other relationships are derived and shown to have simple and natural geometric significance in the new framework. The geometric viewpoint is also found to suggest certain lines of development—such as the use of self-conjugate (’’normal’’) field variables—with no obvious counterpart in the traditional differential formalisms. The formal ideas are illustrated throughout with elementary applications to properties of a simple homogeneous fluid.