Background: The resultant measures of the information content in molecular electronic
states are revisited. In these overall measures the current-related terms complement the probability
functionals of classical Information Theory. The nonclassical Shannon entropy reflects the average
magnitude of the state phase distribution, while the related current term in the complementary
Fisher measure accounts for the average phase-gradient.
Method: These generalized Fisher and Shannon descriptors of the information content in complex
electronic states are applied to determine the phase-equilibria in molecules. The vertical and
horizontal equilibria in molecules, which mark the extrema of the nonclassical and resultant
entropy/information descriptors, respectively, are explored. The requirement, that the resultant
measures have common solutions of the associated extreme entropy/information principles, calls for
the negative sign of the nonclassical gradient measure.
Conclusion: These extrema imply the phase-transformation of molecular electronic states. A
separation of the density (modulus) and current (phase) factors in many-electron states is effected
using the Harriman-Zumbach-Maschke construction of complex antisymmetric states yielding the
specified electron density. A combined description of molecular systems, which accounts for the
density and current degrees-of-freedom of electronic states is summarized and continuity equations
for the state phase and resultant entropy are discussed.