  We have constructed a nonextensive thermodynamic formalism consisting of two
sets of parallel Legendre transformation structures in previous papers. One is
the physical set and the other is the Lagrange set. In this paper we study the
thermodynamic stability criterion with a dual interpretation of the
thermodynamic relations and quantities. By recourse to the assumption that
volume in nonextenstive system is nonadditive, we conclude that it is the
physical pressure that is responsible for the mechanical balance between any
two parts in a given nonextensive system. It is verified that in the physical
set of transformation structures, the stability criterion can be expressed in
terms of heat capacity and isothermal compressibility. We also discuss the
fluctuation theory in nonextensive thermodynamics.
