Formulation of the Hellmann–Feynman theorem for the “second choice” version of Tsallis’ thermostatistics

An approach to formulating the Hellmann–Feynman theorem within the “second choice” formalism of non-extensive statistical mechanics is considered. For the state of thermal equilibrium, we derive a relation of Hellmann–Feynman type between the derivative of the non-extensive free energy with respect to the external parameter and the quantum statistical q-average of the derivative of the Hamilton operator. We also give a proper extension for an arbitrary observable commuting with the Hamiltonian. Some reasons for the usefulness of new formulas are discussed.