Thermodynamic potentials and thermodynamic relations in nonextensive thermodynamics

The generalized Gibbs free energy and enthalpy are derived in the framework of nonextensive thermodynamics by using the concept of the physical temperature and the physical pressure. Some relations of the thermodynamical potentials are changed due to the difference between the physical temperature and the inverse of Lagrange multiplier. We derive the thermodynamical relation between the heat capacities at a constant volume and at a constant pressure using the generalized thermodynamical potential. We find that it has a different form from the traditional one in Gibbs thermodynamics. But, the expressions of the heat capacities in this framework using the generalized thermodynamical potentials are still the same as the traditional one.