In classical mechanics, the exact solution is known for both the seprerate parts of the system and the system as a whole. This allows the energy-difference between these two to be calculated.
In a quantum system, the exact solution of the system is not known. Because of this, the correlation acording to the classical definition is unknown. An aproximate solution allows an nergy-difference, the exchange to be calculated between the seperate parts and the whole system. The energy correction on this, for wich the exact solution needs to be known, is the correlation.