Electronic chemical potential as information temperature

A coupling between the energy and entropy deficiency descriptors of the electron distributions in molecular systems is examined for both the equilibrium ( ground-state) and non-equilibrium ( trial) electron distributions. The Lagrange multipliers of the constrained variational principles in both the energy and missing-information representations, related to the information 'temperature' parameters, are identified. It is demonstrated that the global information temperature, which characterizes the equilibrium electron distribution, is given by the system chemical potential. The non-equilibrium electron densities are shown to require the non-equalized information temperatures, measured by the local chemical potentials. An illustrative case of the hydrogen-like atom is examined in a more detail.