Abstract
The entropy of a positive trace class operator, P, is defined as S(P) = -Tr P log P. We will review known inequalities relating the entropy of the density matrix representing the state of an N-particle system to the entropy of the corresponding reduced density matrices. One important inequality of this type is
where ρ1 is the 1-particle density matrix of the system. The density matrices are normalized so that TrρN = 1 and Trρ1 = N; the upper sign refers to fermions, the lower to bosons, and I denotes the identity operator. We will discuss a conjectured generalization of this inequality to the case of two-particle density matrices. We also conjecture that S(ρ2) ≥ 0 in the case of fermions when the two-particle density matrix, ρ2, is normalized so that \(Tr{\rho _2} = \left( {\begin{array}{*{20}{c}} N \\ 2 \end{array}} \right)\). Evidence for the validity of both conjectures will be presented.
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© 1987 D. Reidel Publishing Company
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Ruskai, M.B. (1987). Entropy of Reduced Density Matrices. In: Erdahl, R., Smith, V.H. (eds) Density Matrices and Density Functionals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3855-7_11
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DOI: https://doi.org/10.1007/978-94-009-3855-7_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8214-3
Online ISBN: 978-94-009-3855-7
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