Assume a binary mixture, with the component $A$ in concentration $c$ and the component $B$ in concentration $1-c$. The total energy $E(c)$ is thus given by a function of one variable $c$ (if we do not take into account the kinetic energy...). Now let's assume that energy has two minima at $c_0$ and $c_1$. The minimization of energy should lead to a phase segreggation.
But : In order for two phases $1$ and $2$ to be at equilibrium, we need two conditions : $\mu_1=\mu_2$ and $\pi_1=\pi_2$. Two equations for 1 variable !! The system is overconstrained and there cannot be any phase segregation. How come the minimization of the energy and basic themodynamics not compatible ?