Thermodynamic stability of multicomponent ideal gas

We present an example counter to the widely-accepted concept on equilibrium states that “Any thermodynamic equilibrium state of two component systems is determined by specifying 4 thermodynamic variables that include at least 1 extensive variable.” which is equivalent to Gibbs’ phase rule. We demonstrate this fact by thought experiments on an A/B binary mixture where temperature, pressure and chemical potential of the A-species are chosen as the 3 intensive variables while the number of B-molecules is chosen as the 1 extensive variable. Our findings also apply to $M(>2)$-component systems.