A system is said to be in equilibrium when the variables of the system have the same values at all points in the system and do not change as a function of time. An equilibrium can be stable, unstable or metastable.
Metastable
equilibrium
Stable equilibrium
Unstable equilibrium
An equilibrium is said to be metastable when a small disturbance of the variables of the system does not modify it but a more significant disturbance causes it to evolve into another state.
Such a state of metastable equilibrium corresponds to a local minimum of the thermodynamic potential.
An equilibrium is said to be stable when a disturbance of the variables which characterizes it does not lead to a modification of this state.
Such a state of stable equilibrium corresponds to the lowest value of the thermodynamic potential.
An equilibrium is said to be unstable when a small disturbance of the variables which characterizes it produce a significant change and leads to the system evolving into another state.
Such an unstable equilibrium corresponds to a maximum of the thermodynamic potential.