The quantum-generalized Information Theory is applied to explore mole- cular equilibrium states by using the resultant information content of electronic states, determind by the classical (probability based) measures and their non -classical (phase/current related) complements, in the extremum entropy/information princi- ples.The“ vertical ”(probability-constrained)entropicrulesareinvestigatedwithinthe familiar Levy and Harriman–Zumbach–Maschke constructions of Density Functional Theory. A close parallelism between the vertical maximum-entropy and minimum- energy principles in quantum mechanics and their thermodynamic analogs is empha- sized and a relation between the probability and phase distributions in the “ horizontal ” (probability-unconstrained) phase -equilibria is examined. These solutions are shown to involve the spatial phase contribution related to the system electron density.The complete specification of the equilibrium states of molecular/promolecular fragments, including the subsystem density and the equilibrium phase of the system as a whole, is advocatedandillustratedforbondedhydrogensinH 2 .Elementsofthe non -equilibrium thermodynamic description of molecular systems are formulated. They recognize the independent probability and phase state parameters, the associated currents, and their contributions to the quantum entropy density and its current. The phase and entropy continuity equations are explored and the local sources of these quantities are identi- fied.