Inequality with Applications in Statistical Mechanics 论文

摘要

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.