Some inequalities and relations among entropies of reduced quantum mechanical density matrices are discussed and proved. While these are not as strong as those available for classical systems they are nonetheless powerful enough to establish the existence of the limiting mean entropy for translationally invariant states of quantum continuous systems.
KeywordsDensity Matrix Disjoint Union Spectral Decomposition Invariant State Selfadjoint Operator
Unable to display preview. Download preview PDF.
- 1.Ruelle, D.: Statistical mechanics. Proposition (7.2.6). New York: W. A. Benjamin 1969. For related results the reader is referred to: A. Huber in “Mathematical Methods in Solid State and Superfluid Theory”, R. C. Clark and G. H. Derrick ed., Oliver and Boyd, Edinburgh, 1969, page 364; H. Falk, “Inequalities of J. W. Gibbs” to appear in Amer. J. Phys., July, 1970.zbMATHGoogle Scholar
- 3.Ruelle, D.: op. cit., Proposition (2.5.4).Google Scholar
- 4.— op. cit., Proposition (2.5.2).Google Scholar