Landau potential
The grand potential is a quantity used in statistical mechanics, especially for irreversible processes in open systems. The grand potential is the characteristic state function for the grand canonical ensemble.
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, ΦG is a minimum. This can be seen by considering that dΦG is zero if the volume is fixed and the temperature and chemical potential have stopped evolving.
Some authors refer to the grand potential as the Landau free energy or Landau potential an write its definition as:
named after Russian physicist Lev Landau, which may be a synonym for the grand potential, depending on system stipulations. For homogeneous systems, one obtains .
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