The Hellmann-Feynman theorem in a pure ensemble is extended to a quasidegenerate mixed ensemble (canonical) as an ensemble average value. The theorem is also extended to a grand canonical ensemble wherein average particle number is conserved. Connections with the thermodynamic observables are made. An approximate relation between $\partial {\left[\widehat{H}\right]}_C∕\partial \lambda$ and $\partial {\left[\widehat{H}\right]}_G∕\partial \lambda$ is established at the leading order of the saddle-point approximation.

• Received 23 October 2006

DOI:https://doi.org/10.1103/PhysRevA.75.032514