Why is Fermi Level constant across pn junction?

[chingkui]

I know this is true under thermal equilibrium, but I am not sure why. Why can't the Fermi level be a function of position relative to the pn-junction? How does that follow from thermodynamics/statistical mechanics?

 

[mfb]

If you have (more than 50% occupancy at energy E) on one side and (less than 50% occupancy at energy E) at the other side, the system is not in equilibrium, and electrons can move from one side to another, increasing entropy and reducing the energy of the system.