Grand potential is defined by
where U is the internal energy, T is the temperature of the system, S is the entropy, μ is the chemical potential, and N is the number of particles in the system.
The change in the grand potential is given by
where P is pressure and V is volume, using the fundamental thermodynamic relation (combined first and second thermodynamic laws);
When the system is in thermodynamic equilibrium, Φ is a minimum. This can be seen by considering that dΦ is zero if the volume is fixed and the temperature and chemical potential have stopped evolving.