Dimension of the Gibbs function topological manifold. II: Thermodynamically stable binary quasicrystals: reality or artefact? (Q2353518)

The author examines the graphical representation of a thermodynamic equilibrium state. He shows the similarity between the Gibbs' phase rule and the Euler theorem on planar graphs on isomorphic surfaces with the surface of a two-dimensional sphere. By choosing an invariant state on a two-dimensional surface, he establishes that the two-phase system and the complex multi-phase systems can be expressed in the form of a set of points and lines. Weighted chemical potentials of individual components are represented by the graph edges. Thus a state of thermodynamic equilibrium can be represented by a graph on a two-dimensional spherical manifold. The graph edges that connect points corresponding to individual degrees of freedom in an equilibrium state have a minimal length. For Part I see [ibid. 53, No. 2, 495--513 (2015; Zbl 1325.80001); erratum ibid. 53, No. 2, 514--516 (2015; Zbl 1325.80003)].