The grand potential or Landau potential or Landau free energy is a quantity used in statistical mechanics, especially for irreversible processes in open systemss. The grand potential is the characteristic state function for the grand canonical ensemble.

Definition

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.

where P is pressure and V is volume, using the fundamental thermodynamic relation (combined first and second thermodynamic lawsWhen the system is in thermodynamic equilibrium is zero if the volume is fixed and the temperature and chemical potential have stopped evolving.

Landau free energy

Some authors refer to the grand potential as the Landau free energy or Landau potential, named after Russian physicist Lev Landau.

Homogeneous systems (vs. inhomogeneous systems)

, for the Gibbs free energy is negative implies that the extraction of particles from the system to the reservoir requires energy input.

Such homogeneous scaling does not exist in many systems. For example, when analyzing the ensemble of electrons in a single molecule or even a piece of metal floating in space, doubling the volume of the space does double the number of electrons in the material. The problem here is that, although electrons and energy are exchanged with a reservoir, the material host is not allowed to change. Generally in small systems, or systems with long range interactions (those outside the thermodynamic limit.

See also

• Gibbs energy

• Helmholtz energy

References

External links

• Grand Potential (Manchester University)