TY - JOUR
ID - 112881
TI - On Selected Properties of the Gibbs Function Topological Manifold
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Turulski, Jan
AD - Third Age University, 16035 Czarna Wies Koscielna, Poland, and
Chemistry Institute, University at Bialystok, 15443, Bialystok, Poland
Y1 - 2022
PY - 2022
VL - 13
IS - 4
SP - 253
EP - 280
KW - Thermodynamic equilibrium
KW - Gibbs function
KW - topological manifold
KW - Graph theory
DO - 10.22052/ijmc.2022.246694.1642
N2 - Quantitatively, the equilibrium in classical thermodynamics in the C-component isobaric-isothermal system is determined by the minimum value of the Gibbs function. The topological manifold of this function is a 2-D dimensional, smooth piece, geometric creation. These pieces represent individual states of single-phase systems. Successive pieces of the manifold are glued along the line of phase transitions to form the manifold of the whole, en bloc, C-component 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 single-phase 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 single-phase 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.
UR - https://ijmc.kashanu.ac.ir/article_112881.html
L1 - https://ijmc.kashanu.ac.ir/article_112881_ccf91230b0ce05a8b215eb9de4f87501.pdf
ER -