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

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  • Rastegin, Alexey E.

Abstract

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.

Suggested Citation

  • Rastegin, Alexey E., 2013. "Formulation of the Hellmann–Feynman theorem for the “second choice” version of Tsallis’ thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 103-110.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:103-110
    DOI: 10.1016/j.physa.2012.08.010
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    1. Ferri, G.L. & Martínez, S. & Plastino, A., 2005. "The role of constraints in Tsallis' nonextensive treatment revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 205-220.
    2. R. K. Niven, 2009. "Combinatorial entropies and statistics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 49-63, July.
    3. Toral, Raúl & Salazar, Rafael, 2002. "Ensemble equivalence for non-extensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 52-57.
    4. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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