Energy dependence on fractional charge for strongly interacting subsystems.

The energies of a pair of strongly interacting subsystems with arbitrary noninteger charges are examined from closed- and open-system perspectives. An ensemble representation of the charge dependence is derived, valid at all interaction strengths. Transforming from resonance-state ionicity to ensemble charge dependence imposes physical constraints on the occupation numbers in the strong-interaction limit. For open systems, the chemical potential is evaluated using microscopic and thermodynamic models, leading to a novel correlation between ground-state charge and an electronic temperature.