Abstract
The geometric properties of the equilibrium manifolds of the thermodynamic system with finite baryon density predicted by the holographic dualities method have been studied in this work. Geometrothermodynamics was used as the formalism of the study, which allows to obtain results invariant with respect to the Legendre transformations, i.e. independently of the choice of thermodynamic potentials. For the considered system, the corresponding metrics and scalar curvatures are calculated, and their properties are also described. To study thermodynamic systems, we calculated the metric of the corresponding equilibrium manifolds, the determinants of the metric tensors, and the corresponding scalar curvatures. Using a holographic approach, strongly interacting quantum systems with a finite baryon density were considered, i.e. systems like quantum chromodynamics. 3D graphs are obtained, which clearly show at what values of thermodynamic variables the scalar curvatures tend to infinity or to zero, which indicates possible phase transitions and possible compensation of interactions by quantum effects, respectively. To establish a reliable connection between the discontinuity lines obtained in this work and phase transitions in the thermodynamic systems defined in thermodynamic systems, additional analysis is required. This analysis can be carried out, for example, when constructing geodesic curves on the considered manifolds.