Correlation

The definition of correlation energy is the difference between the energy given by the mean-field approximation and the actual exact potential energy of a system. The mechanisms that give rise to this gap are inherently different between classical and quantum systems. For example, quantum systems are governed by intrinsic ontic randomness, where the quanta of the system are wavefunctions rather than point particles. This is a contributing factor to correlation energy which is not paralleled in classical mechanics. Quantum systems also demonstrate mechanisms like exchange (from exclusion principle) and entanglement, which diverges the two systems even further from each other.