PROPERTIES OF NONFREENESS: AN ENTROPY MEASURE OF ELECTRON CORRELATION

The "nonfreeness" of a many-fermion state ω is the entropy of ω relative to the free state that has the same 1-particle statistics as ω. 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. However, 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.

[1]  C. Pillet.  Quantum Dynamical Systems , 2006 .

[2]  R. P. Sagar,et al.  Mutual information and electron correlation in momentum space. , 2006, The Journal of chemical physics.

[3]  A. Gottlieb,et al.  New measure of electron correlation. , 2005, Physical review letters.

[4]  R. P. Sagar,et al.  Shannon-information entropy sum as a correlation measure in atomic systems , 2003 .

[5]  D. Petz.  Monotonicity of quantum relative entropy revisited , 2002, quant-ph/0209053.

[6]  P. Gori-Giorgi,et al.  Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion , 2002, cond-mat/0205342.

[7]  V. H. Smith,et al.  The He isoelectronic series and the Hooke’s law model: Correlation measures and modifications of Collins’ conjecture , 1999 .

[8]  P. Fazekas,et al.  Lecture notes on electron correlation and magnetism , 1999 .

[9]  TWO-SITE HUBBARD MODEL, THE BARDEEN-COOPER-SCHRIEFFER MODEL, AND THE CONCEPT OF CORRELATION ENTROPY , 1997 .

[10]  J. Perdew,et al.  CORRELATION ENTROPY OF THE H2 MOLECULE , 1997 .

[11]  Sagar,et al.  Physical interpretation of information entropy: Numerical evidence of the Collins conjecture. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[12]  P. Ziesche.  Correlation strength and information entropy , 1995 .

[13]  Joseph H. Eberly,et al.  Measure of electron-electron correlation in atomic physics , 1994 .

[14]  D. Petz,et al.  Quantum Entropy and Its Use , 1993 .

[15]  Sears,et al.  Some novel characteristics of atomic information entropies. , 1985, Physical review. A, General physics.

[16]  A. Uhlmann.  Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory , 1977 .

[17]  J. Griffin,et al.  Evolution of a quantum system: Lifetime of a determinant , 1976 .

[18]  A. Uhlmann.  The "transition probability" in the state space of a ∗-algebra , 1976 .

[19]  G. Lindblad.  Completely positive maps and entropy inequalities , 1975 .

[20]  G. Lindblad.  Expectations and entropy inequalities for finite quantum systems , 1974 .

[21]  G. Lindblad.  Entropy, information and quantum measurements , 1973 .

[22]  D. Klein,et al.  Perturbation Expansion of the Linear Hubbard Model , 1973 .

[23]  D. Bures.  An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite *-algebras , 1969 .

[24]  W. Kutzelnigg,et al.  Correlation Coefficients for Electronic Wave Functions , 1968 .

[25]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[26]  Philip W. Anderson,et al.  New Approach to the Theory of Superexchange Interactions , 1959 .