In a two-band system, both conventional sign-preserving \(s_{++}\) and unconventional sign-changing \(s_{\pm }\) superconducting state may appear at low temperatures. Moreover, they may transform from one to another due to the impurity scattering. To study the details of such a transition here we derive the expression for the Grand thermodynamic potential \(\Omega\) for a two-band model with nonmagnetic impurities considered in a \(\mathcal {T}\) -matrix approximation. For the iron-based materials within the multiband Eliashberg theory, we show that the \(s_{\pm } \rightarrow s_{++}\) transition in the vicinity of the Born limit is a first order phase transition.
