The entropies of several typical coupled bosonic oscillators are calculated by virtue of the generalized Hellmann–Feynman theorem (GHFT). The relation between GHFT and entropy-variation is construct by using von Neumann entropy, which provides us with a new approach for deriving entropy of some complicated systems.
Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state (TVS) for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann—Feynman theorem and the entroy variation in the context of the TVS.