Use of graph theory in thermodynamics of phase equilibria.

Abstract

A concept to use graph theory for the description of phase equilibria is developed. It is shown that a specific planar graph, called the graph of state, corresponds unequivocally to a specific state of phase equilibrium. Hence, the involved problem of enumeration of different states equilibria in complex systems is simplified to the problem of enumeration of graphs of the specified type. One-phase systems with three independent components can exist in two forms, normal and exotic; while the normal form is of course known also for systems with 1 and 2 components, the exotic form can only exist if the number of components is 3 or more. It can be speculated that stable quasicrystals represent such an exotic form. Assuming the occurrence of all of the thermodynamically allowed processes, the number of one-phase exotic states in systems that consist of tens of bioelements can, intuitively, be used as a measure of Earth's biodiversity.