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Grand potential : ウィキペディア英語版
Grand 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.
==Definition==

Grand potential is defined by
:
\Phi_ \ \stackrel\ U - T S - \mu N

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
:
\begin
d\Phi_ & = dU - TdS - SdT - \mu dN - Nd\mu \\
& = - P dV - S dT - N d\mu
\end

where ''P'' is pressure and ''V'' is volume, using the fundamental thermodynamic relation (combined first and second thermodynamic laws);
:dU = TdS - PdV + \mu dN
When the system is in thermodynamic equilibrium, Φ''G'' is a minimum. This can be seen by considering that dΦ''G'' is zero if the volume is fixed and the temperature and chemical potential have stopped evolving.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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