Inequality with Applications in Statistical Mechanics
- 1 November 1965
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 6 (11) , 1812-1813
- https://doi.org/10.1063/1.1704727
Abstract
We prove for Hermitian matrices (or more generally for completely continuous self‐adjoint linear operators in Hilbert space) A and B that Tr (eA+B) ≤ Tr (eAeB). The inequality is shown to be sharper than the convexity property (0 ≤ α ≤ 1) Tr (eαA+(1−α)B) ≤ [Tr (eA)]α[Tr (eB)]1−α, and its possible use for obtaining upper bounds for the partition function is discussed briefly.Keywords
This publication has 5 references indexed in Scilit:
- Lower Bounds for the Helmholtz FunctionPhysical Review B, 1965
- Free Energy of the Antiferromagnetic Linear ChainPhysical Review B, 1964
- Remark on Weyl's Note “Inequalities Between the Two Kinds of Eigenvalues of a Linear Transformation”Proceedings of the National Academy of Sciences, 1950
- On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations IProceedings of the National Academy of Sciences, 1949
- Inequalities between the Two Kinds of Eigenvalues of a Linear TransformationProceedings of the National Academy of Sciences, 1949