Relationship of Quantum Entanglement to Density Functional Theory

The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is found that the density matrix contains information about both quantum entanglement and phase transitions even though there may not be any direct relationship implied by one on the other.