Thermodynamic properties of the solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation

We study the thermodynamic properties of solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation. First, we study the nonextensive grand canonical distribution function and the nonextensive quantum statistics with the parameter transformation. Then, we derive the generalized Boson distribution and Fermi distribution in the nonextensive quantum statistics. Further, we study the thermodynamic properties of solid and metal electrons in the nonextensive quantum system, including the generalized Debye models, the generalized internal energies, the generalized capacities and chemical potential. We derive new expressions of these thermodynamic quantities, and we show that they all depend significantly on the nonextensive parameter and in the limit they recover to the forms in the classical quantum statistics. These new expressions may be applied to study the characteristics in some nonextensive quantum systems where the long-range interactions and/or long-range correlations play a role.