

On Selected Properties of the Gibbs Function Topological Manifold





نویسنده

Turulski Jan

منبع

Iranian Journal Of Mathematical Chemistry  2022  دوره : 13  شماره : 4  صفحه:253 280



چکیده

Quantitatively, the equilibrium in classical thermodynamics in the ccomponent isobaricisothermal system is determined by the minimum value of the gibbs function. the topological manifold of this function is a 2d dimensional, smooth piece, geometric creation. these pieces represent individual states of singlephase systems. successive pieces of the manifold are glued along the line of phase transitions to form the manifold of the whole, en bloc, ccomponent system. gluing smooth pieces together must guarantee the continuity of the glued whole. the study found the dependence of the number of ways of gluing singlephase pieces on the number of components of the system. it has also been shown that the distribution of components in individual phases of the system is represented by a planar graph with 4 faces, called a normal graph.studies of the topological properties of the manifold fragments representing singlephase equilibrium states indicate that the value of the gibbs potential in these states is encoded in the geometry of the topological manifold. in concrete terms, this value is equal to the length of the minimum path lying on the surface of the manifold, connecting the various degrees of freedom of the system (the vertices of the graph). in complex systems, with very large c, the number of paths connecting the degrees of freedom is monstrously large. preliminary calculations show that in such systems the number of paths with a minimum length or not much different from it may be greater than one.

کلیدواژه

Thermodynamic Equilibrium ,Gibbs Function ,Topological Manifold ,Graph Theory

آدرس

Third Age University, Chemistry InstituteChemistry Institute, Poland

پست الکترونیکی

jan.turulski@protonmail.com












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