Grand potential
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The grand potential is a quantity used in statistical mechanics, especially for irreversible processes in open systems.
Grand potential is defined by
Where E is the 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
- dΦG = − SdT − Ndμ − PdV
Where P is pressure and V is volume.
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.
For an ideal gas,
- ΦG = − kBTln(Ξ) = − kBTZ1eβμ
where Ξ is the grand partition function, kB is Boltzmann constant, Z1 is the partition function for 1 particle and β is equal to 1 / kBT.
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[edit] Landau free energy
Some authors refer to the Landau free energy or Landau potential as:[1][2]
named after Russian physicist Lev Landau, which may be a synonym for the grand potential, depending on system stipulations.
[edit] References
- ^ Lee, Joon Chang. (2002) book Thermal Physics - Entropy and Free Energies (ch. 5). New Jersey: World Scientific
- ^ Reference on "Landau potential" is found in the book States of Matter by David Goodstein (page 19) as
where F is the Helmholtz free energy. For homogeneous systems, one obtains 
