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Examining phase stabilities and phase equilibria in strongly correlatedmaterials asks for a next level in the many-body extensions to thelocal-density approximation (LDA) beyond mainly spectroscopic assessments. Herewe put the charge-self-consistent LDA+dynamical mean-field theory (DMFT)methodology based on projected local orbitals for the LDA+DMFT interface and atailored pseudopotential framework into action in order to address suchthermodynamics of realistic strongly correlated systems. Namely a case studyfor the electronic phase diagram of the well-known prototype Mott-phenomenasystem V$_2$O$_3$ at higher temperatures is presented. We are able to describethe first-order metal-to-insulator transitions with negative pressure andtemperature from the self-consistent computation of the correlated total energyin line with experimental findings.

Approaching finite-temperature phase diagrams of strongly correlated materials: a case study for V2O3