nonfreeness: an entropy measure of electron correlation

“Nonfreeness” is the (negative of the) difference between the von Neumann entropies of a given many-fermion state and the free state that has the same 1-particle statistics. It also equals the relative entropy of the two states in question, i.e., it is the entropy of the given state relative to the corresponding free state. The nonfreeness of a pure state is the same as its “particle-hole symmetric correlation entropy”, a variant of an established measure of electron correlation. But nonfreeness is also defined for mixed states, and this allows one to compare the nonfreeness of subsystems to the nonfreeness of the whole. Nonfreeness of a part does not exceed that in the whole; nonfreeness is additive over independent subsystems; and nonfreeness is superadditive over subsystems that are independent on the 1-particle level. The word “correlation” in the context of many-electron systems is somewhat overcharged and ambiguous, except when used in the expression “correlation energy,” where it refers to the difference between the energy of the true ground state of a many-electron system and the Wolfgang Pauli Institute, Nordbergstr. 15, A–1090 Wien, Austria ([email protected]). WPI c/o Fak. f. Math., Univ. Wien, Nordbergstr. 15, A–1090 Wien, ([email protected]).