I have a question concerning the following picture that is given in the german wikipedia:Gibbs Free Energy at a Phase Transition
Depicted are different observables of 3 thermodynamic systems, in the first column you can see the Gibbs Free Energy (G), depicted vs the temperature (T), at constant pressure. Lines in black indicate the actual function of G, whereas lines in grey depict the value of G that the other phase would have at that temperature and pressure.
To me it seems that a system that can choose between two phases with different Gibbs Free Energy will choose the phase with bigger Gibbs Free Energy, which is a contradiction to what I would expect the system to behave.
What I thought was, that the system always wants to reach the thermodynamic equilibrium by minimizing the thermodynamical potential. Can somebody clarify the situation for me?