# Does minimizing ANY type of energy ALWAYS predict a state of equilibrium?

My intuition says no, but I am having trouble coming up with concrete examples.

I know that minimizing Gibbs free energy predicts a state of equilibrium, while minimizing kinetic or internal energy does not correspond to equilibrium. However, I am not so sure about potential energy--- when PE is at a minimum, is the system also at equilibrium?

• If you write a wavefunction of H$_2^+$ molecule concentrating at nuclei, e.g. $\delta(r-R)$, the potential energy is minimized. By the uncertainty principle, the kinetic energy is quite large. This wavefunction neither corresponds to the ground state of H$_2^+$ nor the ground state/equilibrium of an ensemble H$_2^+$ molecules. – user26143 Dec 8 '13 at 7:07
• If you minimize Gibbs free energy, than you have equilibrium at constant pressure and temperature, etc... so the type of energy you choose corresponds to given ensemble. Roughly speaking. – ssavec Dec 9 '13 at 12:53
• No. None of the thermodynamic potentials is at its minimum at the equilibrium point of ANY system. This includes G. – sencer Dec 10 '13 at 2:49