Can States of Thermodynamic Equilibrium in Complex Chemical Systems Be Degenerate?

In this paper, we consider thermodynamic single-phase closed systems under isothermal and isobaric conditions. The state of such systems is characterized by parameters such as pressure, composition, etc., which are called degrees of freedom of the system. If the system is in thermodynamic equilibrium, then for these parameters, the value of the Gibbs function, DG, reaches a minimum value equal to the sum of the weighted chemical potentials of the individual components. The presented work shows that in complex chemical systems there may be many sets of chemical potentials giving the same value of DG, i.e., the equilibrium state is degenerate. A relationship between the maximum value of the degree of degeneracy and the composition has been found. From a topological point of view, the state of the system is represented by a planar graph lying on the surface of the topological manifold DG, formed by a path/paths of minimum length connecting all degrees of freedom of the system (vertices of the graph). Individual paths are a concatenation of edges connecting successive pairs of degrees of freedom. The length of the graph edges is equal to the weighted value of the chemical potential of the corresponding component of the system. The number of paths increases rapidly with the increase in the number of components of the system. The number of paths of minimum length depends on the configuration of the degrees of freedom of the system. In the study of model ternary systems with randomly selected 51 configurations of degrees of freedom, it was shown that in such systems only about 75% of configurations have one path of minimum length, while the rest are characterized by the existence of two or more minimum or near-minimum paths. This indicates that among ternary systems there are some in which the equilibrium state is degenerate. According to the topological representation of equilibrium states in complex systems, the degeneration of these states is a consequence of the existence of a large number of paths in such systems.