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Generalized Feynman-Hellmann theorem for ensemble average values

Hong-Yi Fan, Bo-zhan Chen

Physics Letters AJul 1, 199527 citations

Statistical properties of the Hamiltonian generating phase state derived by using the generalized Hellmann–Feynman theorem

Hong-Yi Fan, Xue-xiang Xu, Liyun Hu

Physica A Statistical Mechanics and its ApplicationsJan 5, 20103 citations

On the Hellmann-Feynman theorem in statistical mechanics

Paolo Amore, Francisco Marcelo Fernández

arXiv:2004.04018Physics Letters AMay 11, 20202 citations

Hellmann-Feynman theorem in a mixed ensemble

Dhurba Rai

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 $\ensuremath{\partial}{[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}]}_{C}∕\ensuremath{\partial}\ensuremath{\lambda}$ and $\ensuremath{\partial}{[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}]}_{G}∕\ensuremath{\partial}\ensuremath{\lambda}$ is established at the leading order of the saddle-point approximation.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 $\ensuremath{\partial}{[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}]}_{C}∕\ensuremath{\partial}\ensuremath{\lambda}$ and $\ensuremath{\partial}{[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}]}_{G}∕\ensuremath{\partial}\ensuremath{\lambda}$ is established at the leading order of the saddle-point approximation.

Physical Review AMar 21, 20079 citations

Application of generalized Hellmann-Feynman theorem in deriving internal energy of some Hamiltonians in quantum optics

Hong-Yi Fan, Min Wang, Peng Yan

In this paper, after introducing the generalized Hellmann-Feynman (or Feynman-Hellmann) theorem (GHFT) for mixed-state ensemble average, we apply GHFT to deriving the internal energy of some Hamiltonian systems in quantum optics. The ensemble average energy contributed from each separated term involved in the Hamiltonian is also considered. We thus develop an alternate approach for deriving the internal energy.

Il Nuovo Cimento BJun 1, 20060 citations

Entropy-variation with resistance in a quantized RLC circuit derived by the generalized Hellmann–Feynman theorem

Fan Hong-Yi, Xue-xiang Xu, Liyun Hu

By virtue of the generalized Hellmann–Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance–inductance–capacitance (RLC) electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.

arXiv:0905.0246Chinese Physics BJun 1, 20106 citations

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

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

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