Generalized Hellmann-Feynman Theorem for Ensemble Average Expressed in the Formalism of Pure State Expectation

Abstract

We show that the generalized Hellmann-Feynman theorem (GHFT) for ensemble average can be expressed in the formalism of pure state expectation. We employ the thermo field dynamics proposed by Umezawa and Takahash to realize this goal, the pure state |0(β)〉 is defined in doubled eigenvector space of the Hamiltonian. Relation between the GHFT and entropy-variation in the context of |0(β)〉 is also derived.